This paper is concerned with the stochastic stabilizability problem of Markovian jump systems with state and i...
Kang Yu1,2 1.Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,P.R.China2.Department of Automation,University of Science and Technology of China,Hefei 230026,P.R.China
This paper studies the reachability problem of the switched linear discrete singular (SLDS) systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based on a peculiar repeatedly introduced switching sequence. The necessary and sufficient conditions are obtained for the reachability of the SLDS systems.
This paper addresses the stability issue of switched linear systems with perturbed switching paths. First, by introducing the notions of child-path and parent-path, we are able to define the distance between two switching paths by means of their switching matrices chains. Next, we present the nice properties of the defined distance. Then, a stability criterion is presented for a class of switched linear systems with perturbed switching paths. Finally, an illustrative example is presented to verify the effectiveness of the approach.
In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of (practical) stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, (a) an (practical) SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded (practical) SISS subsystems.
The admissibility analysis and robust admissible control problem of the uncertain discrete-time switched linear singular (SLS) systems for arbitrary switching laws are investigated. Based on linear matrix inequalities, some sufficient conditions are given for: A) the existence of generalized common Lyapunov solution and the admissibility of the SLS systems for arbitrary switching laws, B) the existence of static output feedback control laws ensuring the admissibility of the closed-loop SLS systems for arbitrary switching laws and norm-bounded uncertainties.
