Admissibility and static output‐feedback stabilization of singular Markovian jump systems with defective statistics of modes transitions

Abstract

SummaryThis paper presents a necessary and sufficient condition for discrete‐time singular Markovian jump linear systems with defective statistics of modes transitions to be regular, causal, and stochastically stable. The static output‐feedback stabilization problem for discrete‐time singular Markovian jump linear system with defective statistics of modes transitions is studied. Furthermore, the defective statistics about modes transitions are studied by considering the uncertain transition probabilities and partially unknown transition probabilities situations account in a composite way. The closed‐loop system is represented in an augmented form, in which input and gain‐output matrices are separated. By virtue of the system augmentation, a sufficient condition for the existence of desired controllers is established. An extension to mode‐independent static output‐feed stabilization is provided as well. Copyright © 2013 John Wiley & Sons, Ltd.

Comments on ‘Admissibility and static output‐feedback stabilization of singular Markovian jump systems with defective statistics of modes transitions’

“…In the proof of the sufficiency of Theorem 3.3 in the work of Liu et al, by using the transformation ζ ( k )= N i x ( k ), the authors claim that the stochastic stability of system (3), ie, is equivalent to that of system (15). However, the authors have confused E i and E r ( k ) .…”

“…In this section, a new linear matrix inequality (LMI) is proposed. It is shown that it is equivalent to the stochastic admissibility of the type of singular model addressed in the work of Liu et al but with a different assumption (see Assumption in the following).…”

“…Let the system be a Markov jump linear singular system with rank , and denote by Π=( π i j ) 1≤ i , j ≤ s the transition probability matrix of the Markov chain r ( k ). Consider the same definition of stochastic admissibility as given by Liu et al…”

Sliding mode control for descriptor Markovian jump systems with mode-dependent derivative-term coefficient

“…When descriptor systems are subjected to stochastic disturbance in their structures, it is reasonable to cast the model into descriptor Markovian jump systems. Recently, a great deal of attention has been devoted to descriptor Markovian jump systems, to name a few, stability and stabilization (e.g., [25][26][27][28][29][30][31]), guaranteed cost control and H ∞ control (e.g., [22]), observer design (e.g., [32]) and monographs [33,34]. Among these published results, Wang and Zhang [28] studied the robust control problem for a class of uncertain singular stochastic Markovian jump systems via proportional-derivative state feedback controllers, but the derivative-term coefficient is assumed to be normalized which can be transformed into the standard state-space Markovian jump systems.…”

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