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EN
In this study, a novel robust H[infinity] output feedback control scheme is presented for discrete-time piecewise affine (PWA) systems in the presence of time-varying uncertainties, external disturbance and time-domain constraints. The suggested control method is formulated as linear matrix inequalities (LMIs). The basic idea of them is to construct piecewise quadratic Lyapunov function and introduce a dissipation inequality to guarantee the system energy dissipation. The designed controllers not only guarantee the stability of the closed-loop systems, but also obtain the disturbance attenuation ability.
PL
Zaprezentowano nowy odporny układ sterowania ze sprzężeniem typu H[nieskończoność] do systemów PWA. Uwzględniono obecność zmiennych w czasie niepewności, zewnętrznych zakłóceń i czasowo zależnych wymuszeń.
PL
W artykule przeprowadzono dyskusję typowych warunków przesuwalności biegunów układów liniowych za pomocą statycznych sprzężeń zwrotnych od wyjścia. Jako typowe warunki wystarczające przesuwalności biegunów rozważono warunki Kimury [12] i Wanga [20]. Dla ilustracji problemu rozważono dyskretne zbiory punktów, którym odpowiada określona liczba wejść i wyjść układu. Dla różnych wartości n (4, 6, 7, 8, 9, 10, 12, 16) zaznaczono granice obszarów spełniających warunki Kimury oraz Wanga. Przeanalizowano właściwości poszczególnych obszarów oraz obliczono liczbę Schuberta [3] dla wybranych punktów szczególnych, badając tym samym, czy układy o tych wymiarach mają generycznie właściwość pełnej przesuwalności biegunów.
EN
The paper discusses typical pole assignability conditions for linear time invariant systems, using static output feedback. As typical sufficient assignability conditions the theorems of Kimura [12] and Wang [2] are taken under consideration. For illustration of the problem, discrete sets of points with number of inputs and outputs as coordinates are considered. This is shown for various system degree of 4, 6, 7, 8, 9, 10, 12, 16 with marking of domains in which Kimura and Wang conditions are satisfied. Properties of subsequent domains are analyzed and for specific critical cases the Schubert number [3] is calculated for deciding if real pole placement map is generically surjective for those system dimensions.
EN
Necessary and sufficient conditions of feasibility of second-order linear matrix inequality systems reducible to two or three scalar quadratic inequalities are presented. These conditions are applied to the problem of static output feedback-based stabilization of a second-order system to obtain two feasibility criteria. The first one is based on the general theorems; the second one is tailored specifically for this problem and is easier to use.
4
Content available remote Fault tolerant control design for polytopic LPV systems
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.
5
Content available remote Single stage algorithms for pole placement using static output feedback
EN
Paper presents effective formulae, enabling transfer matrix pole assignment. This is accomplished by the use of generalized matrix inverses and the Kronecker product. All the desired pole distributions are covered - namely simple and multiple, real and complex. On this basis one-stage algorithms were developed, avoiding commonly used reduced orthogonality condition. Computational example of the presented algorithms is given.
6
Content available remote Non-iterative LMI output feedback controller design
EN
The paper addresses the problem of output feedback controller design for linear continuous and discrete-time systems using non-iterative linear matrix inequality (LMI) procedure with guaranteed cost. Numerical examples are given to illustrate the effectiveness of the proposed method.
7
EN
The text covers an in-depth study on the order of the compensator applied in a feedback system for stabilization of the linear, time-invariant, n-th order, multivariable plant. It is shown that all such compensators evolve from the n-th order structure depicted in two forms in Fig. 2 (dotted lines). Presentation includes the so-called reduced and subreduced order compensators and the case of a static output feedback, i.e. the compensator of order zero. All theoretical considerations are supported by examples, in which various types of compensators are synthesized.
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