Feedback Stabilization of Markov Jump Linear Systems with Time-Varying Delay

Abstract

A problem of feedback stabilization of hybrid systems with time-varying delay and Markovian switching is considered. Sufficient conditions for stability based on linear matrix inequalities (LMIs) for stochastic asymptotic stability is obtained. The stability result depended on the mode of the system and of delay-independent. The robustness results of such stability concept against all admissible uncertainties are also investigated. An example is given to demonstrate the obtained results.

Delay-Dependent Criteria for Robust Stabilization of Markovian Switching Networks with Time-Varying Delay

“…There has been an attempt made to establish the infinitesimal generator in [22] for a special Lyapunov functional and also it has been used without an established result in [23,25,26]. We established such an infinitesimal generator with a rigorous proof in [9]. Below, we provide this lemma without proof.…”

“…The MJLS are dynamical systems subject to abrupt variations in their structures. Since MJLS is natural to represent dynamical systems that are often inherently vulnerable to component failures, sudden disturbances, change of internal interconnections, and abrupt variations in operating conditions, they are an important class of stochastic dynamical systems [3][4][5][6][7][8][9][10][11][12][13] and the references therein.…”

Optimal Guaranteed Cost Control of Stochastic Discrete-Time Systems with States and Input Dependent Noise Under Markovian Switching

“…Consider the problem of stabilizing a switched, discrete-time system given by (1) and an associated cost function (6).The system desciptors are …”

“…The Markov jump linear systems (MJLSs) are dynamical systems subject to abrupt variations in their structures. It is known that the MJLS is ideal to represent dynamical systems that are often inherently vulnerable to component failures, sudden disturbances, change of internal interconnections, and abrupt variations in operating conditions ( [1][2][3][4][5][6][7][8][9][10][11], and references therein). On the other hand, discrete-time stochastic processes is found in wide variety of applications, particularly in modeling of engineering, biological, medical and physical systems which are subject to random perturbations [12,13].…”

“…The feedback stability and stabilizability of discrete-time Markov jump linear systems have been studied in two categories: systems with delay and systems without delay. For systems with delay, the readers should refer to ( [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]) and for systems without delay see [21][22][23][24] and references therein.…”