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1
Content available Fault detection based on Lyapunov exponents estimation for stabilized mechanical systems
Puzyrov Volodymyr, Acho Leonardo, Pujol Gisela, Rodellar José
Journal of Theoretical and Applied Mechanics
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2019
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Vol. 57 nr 2
519--531
EN
We study a stabilizable mechanical system in the vicinity of an equilibrium position. This position, as a rule, is unstable, and the system is underactuated. It is assumed that faults affect the technical process and its control. We suggest a fault diagnosis technique based on estimation of Lyapunov characteristic exponents of measured variables. A model of a linear switching system is involved for the system with faults description, and a common quadratic Lyapunov function is used to evaluate the deviation of the maximum exponent with respect to the default system. A scheme of fault magnitude estimation is suggested related to the degree of this deviation. An example of a 2-degree of freedom system is presented to illustrate the procedure.
2
Content available On the existence of a common solution to the Lyapunov equations
Białas S., Góra M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2015
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Vol. 63, nr 1
163-–168
EN
In this paper, a system of Lyapunov equations A*i P + PAi = −Qi (i = 1, . . . ,m), (A) is considered in which Ai are given n × n complex matrices, Qi are unknown n × n Hermitian positive definite matrices and P, if any, is a common solution to the Lyapunov equations (A). Both sufficient and necessary and sufficient conditions are derived for the existence of such a matrix P. Examples are presented to illustrate the results.
3
Content available Robust switched controller design for linear continuous-time systems
Ilka A., Veselý P.
Archives of Control Sciences
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2015
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Vol. 25, no. 4
401--416
EN
In this paper we study a novel approach to the design of a robust switched controller for continuous-time systems described by a novel robust plant model using quadratic stability and multi parameter dependent quadratic stability approaches. In the proposed design procedure with an output feedback a novel quadratic cost function is proposed which allows to obtain different performance dependence on the working points. Finally a numerical examples are investigated.
4
Content available Local analysis of hybrid systems on polyhedral sets with state-dependent switching
Leth J., Wisniewski R.
International Journal of Applied Mathematics and Computer Science
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2014
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Vol. 24, no. 2
341--355
EN
This paper deals with stability analysis of hybrid systems. Various stability concepts related to hybrid systems are introduced. The paper advocates a local analysis. It involves the equivalence relation generated by reset maps of a hybrid system. To establish a tangible method for stability analysis, we introduce the notion of a chart, which locally reduces the complexity of the hybrid system. In a chart, a hybrid system is particularly simple and can be analyzed with the use of methods borrowed from the theory of differential inclusions. Thus, the main contribution of this paper is to show how stability of a hybrid system can be reduced to a specialization of the well established stability theory of differential inclusions. A number of examples illustrate the concepts introduced in the paper.
5
Content available On the stability of continuous-time positive switched systems with rank one difference
Fornasini E., Valcher M. E.
Control and Cybernetics
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2013
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Vol. 42, no. 1
47--62
EN
Continuous-time positive systems, switching among p subsystems whose matrices differ by a rank one matrix, are introduced, and a complete characterization of the existence of a common linear copositive Lyapunov function for all the subsystems is provided. Also, for this class of systems it is proved that a well-known necessary condition for asymptotic stability, namely the fact that All convex combinations of the system matrices are Hurwitz, becomes equivalent to the generally weaker condition that the systems matrices are Hurwitz. In the special case of two-dimensional systems, this allows for drawing a complete characterization of asymptotic stability. Finally, the case when there are only two subsystems, possibly with commuting matrices, is investigated.
6
Content available Simple sufficient conditions for asymptotic stability of positive linear systems for any switchings
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2013
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Vol. 61, nr 2
343--347
EN
The asymptotic stability of positive switched linear systems for any switchings is addressed. Simple sufficient conditions for the asymptotic stability of positive switched continuous-time and discrete-time linear systems are established. It is shown that the positive switched continuous-time (discrete-time) system is asymptotically stable for any switchings if the sum of entries of every column of the matrices of subsystems is negative (less than 1)
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