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1
Content available remote Numerical methods for solving the modified filter algebraic riccati Elquation for H-infinity filtering
Horváth Zsolt
Przegląd Elektrotechniczny
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2019
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R. 95, nr 4
9--15
EN
This paper presents numerical methods for solving the Modified Filter Algebraic Riccati Equation (MFARE) for synthesis of H-infinity fault detection filters. Two methods are presented, namely the gamma-iteration and then rewriting the MFARE in Linear Matrix Inequalities (LMIs) and casting it as a convex optimization problem. Each algorithm has to ensure the condition for a global convergence and also has to deliver an optimal solution. Not at least the computational cost has to be as small as possible.
PL
Zaprezentowano metodę numeryczną rozwiązywania równania MFARE (Modified Filter Algebraic Riccati Equation). Badano dwie metody – iterację gamma i przepisywanie równania w postać Linear Matrix Inequantities.
2
Content available Robust stabilization using a sampled-data strategy of uncertain neutral state-delayed systems subject to input limitations
El Fezazi N., El Haoussi F., Tissir E. H., Alvarez T., Tadeo F.
International Journal of Applied Mathematics and Computer Science
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2018
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Vol. 28, no. 1
111--122
EN
Stabilization of neutral systems with state delay is considered in the presence of uncertainty and input limitations in magnitude. The proposed solution is based on simultaneously characterizing a set of stabilizing controllers and the associated admissible initial conditions through the use of a free weighting matrix approach. From this mathematical characterization, state feedback gains that ensure a large set of admissible initial conditions are calculated by solving an optimization problem with LMI constraints. Some examples are presented to compare the results with previous approaches in the literature.
3
Content available Optimal robust stabilizer design based on UPFC for interconnected power systems considering time delay
Koofigar H. R., Isazadeh G.
Archives of Electrical Engineering
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2017
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Vol. 66, nr 3
459--474
EN
A robust auxiliary wide area damping controller is proposed for a unified power flow controller (UPFC). The mixed H2 /H∞ problem with regional pole placement, resolved by linear matrix inequality (LMI), is applied for controller design. Based on modal analysis, the optimal wide area input signals for the controller are selected. The time delay of input signals, due to electrical distance from the UPFC location is taken into account in the design procedure. The proposed controller is applied to a multimachine interconnected power system from the IRAN power grid. It is shown that the both transient and dynamic stability are significantly improved despite different disturbances and loading conditions.
4
Content available Adaptive observer-based fault estimation for a class of Lipschitz nonlinear systems
Oucief N., Tadjine M., Labiod S.
Archives of Control Sciences
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2016
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Vol. 26, no. 2
245--259
EN
Fault input channels represent a major challenge for observer design for fault estimation. Most works in this field assume that faults enter in such a way that the transfer functions between these faults and a number of measured outputs are strictly positive real (SPR), that is, the observer matching condition is satisfied. This paper presents a systematic approach to adaptive observer design for joint estimation of the state and faults when the SPR requirement is not verified. The proposed method deals with a class of Lipschitz nonlinear systems subjected to piecewise constant multiplicative faults. The novelty of the proposed approach is that it uses a rank condition similar to the observer matching condition to construct the adaptation law used to obtain fault estimates. The problem of finding the adaptive observer matrices is formulated as a Linear Matrix Inequality (LMI) optimization problem. The proposed scheme is tested on the nonlinear model of a single link flexible joint robot system.
5
Content available Methods of controller synthesis using linear matrix inequalities and model predictive control
Miller A., Rybczak M.
Zeszyty Naukowe Akademii Morskiej w Szczecinie
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2015
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nr 43 (115)
22--28
EN
Controllers based on linear matrix inequalities (LMI) and model predictive control (MPC) both use optimization methods; there are however significant differences between them. In case of LMI controllers, optimization is carried out during controller synthesis, because LMI’s are an optimization tool that requires a linear programming problem being solved. With MPC controllers, however, optimization methods are not used as much in controller synthesis as in controller algorithm operation, to determine optimal control signal values based on the found minimum of the criteria function. A square function is used with boundaries from above and below, which requires a square programming problem, with boundaries for decision variables, being solved. In this paper controller synthesis methods using LMI and MPC are shown, with a focus on the steps that need to be performed, and a comparison of both methods.
6
Content available Bounded linear stability region in Linear Matrix Inequalities for a multivariable object
Rybczak M.
Zeszyty Naukowe / Akademia Morska w Szczecinie
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2014
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nr 39 (111)
133--139
EN
This paper is devoted to the concept of stability in linear matrix inequalities. Especially to the analysis of a bounded stability region for a multivariable 3DOF system. The study is focused on two different, user defined, bounded LMI regions where poles are calculated with the use on an algorithm and placed in the left half plane of complex variable plane s. It is shown that in the studied case the shape of the region is irrelevant compared to the location of region bounds. And more specifically only the active bounds where the poles are located on it’s limits are significant to controller operation.
7
Content available Stabilization of autonomous linear time invariant fractional order derivative switched systems with different derivative in subsystems
Balochian S.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2014
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Vol. 62, nr 3
495--503
EN
In this paper, the stabilization problem of a autonomous linear time invariant fractional order (LTI-FO) switched system with different derivative order in subsystems is outlined. First, necessary and sufficient condition for stability of an LTI-FO switched system with different derivative order in subsystems based on the convex analysis and linear matrix inequality (LMI) for two subsystems is presented and proved. Also, sufficient condition for stability of an LTI-FO switched system with different derivative order in subsystems for more than two subsystems is proved. Then a sliding sector is designed for each subsystem of the LTI-FO switched system. Finally, a switching control law is designed to switch the LTI-FO switched system among subsystems to ensure the decrease of the norm of the switched system. Simulation results are given to show the effectiveness of the proposed variable structure controller.
8
Content available Decentralized design of interconnected H infinity feedback control systems with quantized signals
Zhai G., Chen N., Gui W.
International Journal of Applied Mathematics and Computer Science
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2013
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Vol. 23, no. 2
317--325
EN
In this paper, we consider the design of interconnected H infinity feedback control systems with quantized signals. We assume that a decentralized dynamic output feedback has been designed for an interconnected continuous-time LTI system so that the closed-loop system is stable and a desired H infinity disturbance attenuation level is achieved, and that the subsystem measurement outputs are quantized before they are passed to the local controllers. We propose a local-output-dependent strategy for updating the parameters of the quantizers, so that the overall closed-loop system is asymptotically stable and achieves the same H infinity disturbance attenuation level. Both the pre-designed controllers and the parameters of the quantizers are constructed in a decentralized manner, depending on local measurement outputs.
9
Content available remote Innowacyjne rozwiązania w dziedzinie zrównoważonego budownictwa jako pionierskiego rynku Unii Europejskiej
Wall S.
Materiały Budowlane
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2011
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nr 12
36-37
10
Content available remote LMI-based adaptive fuzzy integral sliding mode control of mismatched uncertain systems
Mnasri C., Gasmi M.
International Journal of Applied Mathematics and Computer Science
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2011
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Vol. 21, no 4
605-615
EN
Integral sliding mode design is considered for a class of uncertain systems in the presence of mismatched uncertainties in both state and input matrices, as well as norm-bounded nonlinearities and external disturbances. A sufficient condition for the robust stability of the sliding manifold is derived by means of linear matrix inequalities. The initial existence of the sliding mode is guaranteed by the proposed control law. The improvement of the proposed control scheme performances, such as chattering elimination and estimation of norm bounds of uncertainties, is then considered with the application of an adaptive fuzzy integral sliding mode control law. The validity and efficiency of the proposed approaches are investigated through a sixth order uncertain mechanical system.
11
Content available remote A unified approach to stability analysis of switched linear descriptor systems under arbitrary switching
Zhai G., Xu X.
International Journal of Applied Mathematics and Computer Science
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2010
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Vol. 20, no 2
249-259
EN
We establish a unified approach to stability analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for the stability of all subsystems, then the switched system is stable under arbitrary switching. The analysis results are natural extensions of the existing results for switched linear state space systems.
12
Content available remote A matrix inequality based design method for consensus problems in multi-agent systems
Zhai G., Okuno S., Imae J., Kobayashi T.
International Journal of Applied Mathematics and Computer Science
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2009
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Vol. 19, no 4
639-646
EN
In this paper, we study a consensus problem in multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. The existing design methods found in the literature are mostly based on a graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods cannot deal with complicated control specification. For this purpose, we propose to reduce the consensus problem at hand to the solving of a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and we propose two algorithms for solving the matrix inequality. It turns out that this method includes the existing Laplacian based method as a special case and can deal with various additional control requirements such as the convergence rate and actuator constraints.
13
Content available remote Positivity and stabilization of fractional 2D Roesser model by state-feedbacks, LMI approach
Kaczorek T.
Archives of Control Sciences
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2009
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Vol. 19, no. 2
165-177
EN
LMI approach is applied to compute a gain matrix of state-feedbacks such that the closed-loop system is positive and asymptotically stable. Necessary and suffiecient conditions for the solvability of the problem are established. The proposed method is illustrated by two numerical examples.
14
Content available remote Application of LMI for design of digital control systems
Królikowski A., Horla D.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2008
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Vol. 56, nr 4
361-365
EN
The paper considers a digital design of time-invariant systems in the case of step-invariant (ZOH), bilinear (Tustin’s) and fractional order hold (FROH) discretization methods. The design problem is formulated as linear matrix inequalities (LMI). A closed-loop stability of the digitally designed control systems is discussed.
15
Content available remote Fault tolerant control design for polytopic LPV systems
Rodrigues M., Theilliol D., Aberkane S., Sauter D.
International Journal of Applied Mathematics and Computer Science
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2007
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Vol. 17, no 1
27-37
EN
This paper deals with a Fault Tolerant Control (FTC) strategy for polytopic Linear Parameter Varying (LPV) systems. The main contribution consists in the design of a Static Output Feedback (SOF) dedicated to such systems in the presence of multiple actuator faults/failures. The controllers are synthesized through Linear Matrix Inequalities (LMIs) in both faultfree and faulty cases in order to preserve the system closed-loop stability. Hence, this paper provides a new sufficient (but not necessary) condition for the solvability of the stabilizing output feedback control problem. An example illustrates the effectiveness and performances of the proposed FTC method.
16
Content available remote On the alternative stability criteria for positive systems
Twardy M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2007
|
Vol. 55, nr 4
379-383
EN
The paper discusses the stability problem for continuous time and discrete time positive systems. An alternative formulation of stability criteria for positive systems has been proposed. The results are based on a theorem of alternatives for linear matrix inequality (LMI) feasibility problem, which is a particular case of the duality theory for semidefinite programming problems.
17
Content available remote LMI-based strategies for designing observers and unknown input observers for non-linear discrete-time systems
Korbicz J., Witczak M., Puig V.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2007
|
Vol. 55, nr 1
31-42
EN
The paper deals wit h the problems of designing observers and unknown input observers for discrete-time Lipschitz non-linear systems. In particular, with the use of the Lyapunov method, three different convergence criteria of the observer are developed. Based on the achieved results, three different design procedures are proposed. Then, it is shown how to extend the proposed approach to the systems with unknown inputs. The final part of the paper presents illustrative examples that confirm the effectiveness of the proposed tech-niques. The paper also presents a MATLAB@ function that implements one of the design procedures.
18
Content available remote An LMI approach to checking stability of 2D positive systems
Twardy M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2007
|
Vol. 55, nr 4
385-395
EN
Two-dimensional (2D) positive systems are 2D state-space models whose state, input and output variables take only nonnegative values. In the paper we explore how linear matrix inequalities (LMIs) can be used to address the stability problem for 2D positive systems. Necessary and sufficient conditions for the stability of positive systems have been provided. The results have been obtained for most popular models of 2D positive systems, that is: Roesser model, both Fornasini-Marchesini models (FF-MM and SF-MM) and for the general model.
19
Content available remote A LMI approach to design controller for an induction motor
Koziński W.
Przegląd Elektrotechniczny
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2004
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R. 80, nr 4
380-384
EN
The paper presents Linear Matrix Inequality (LMI) approach to design one of vital parts of controller for an induction motor. From widely accepted induction motor model subplant describing stator current behavior is selected. It forms polytope model with rotor speed as parameter. The parameter should be measurable. The optimization approach with shaping filters is used to design linear parameter varying controllers. At the end of the paper an example is presented.
PL
W artykule przedstawiono zastosowanie liniowych nierówności macierzowych (LMI) do zaprojektowania jednej składowej części regulatora dla silnika indukcyjnego. Z modelu silnika indukcyjnego wydzielono podsystem opisujący zachowanie się prądów stojana. Używając optymalizacyjnej procedury projektowania otrzymano regulator prądu, zmienny w czasie, z prędkością obrotową wirnika jako wielkością sterującą.
20
Stability and controllability properties of extended discrete linear repetitive processes.
Gałkowski K., Sulikowski B., Paszke W., Rogers E., Owens D.
Prace Naukowe Instytutu Cybernetyki Technicznej Politechniki Wrocławskiej. Konferencje
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2001
|
Vol. 103, nr 47
5-14
EN
This paper develops an extension of the state space model for discrete linear repetitive processes which, in addition to their theoretical interest, are also relevant to robotics applications. In particular, the effects of an additional term in the basie state space model of these processes, which represents a direct cross-dependence between successive passes, are investigated. The main results given are the extensions of the existing 2D global-state, and ID equivalent state space model approaches to stability and controllability analysis of this new model. Finally, the role of MATLAB based numerical analysis in this context is also illustrated.
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