Stability of nonlinear stochastic Markov jump system with mode-dependent delays and applications

Stability analysis of delayed Markovian jump systems with delay switching and state signals and applications

“…The main contributions of this article are as follows: (1) A model on delayed MJSs with delay switching and state signals is proposed, where delay switching brings great difficulties to system analysis and synthesis. This phenomenon is very different from the situations that only system state experiences delays, see, for example, References 15,16,21,24,27‐30, where only a few of the above mentioned references are listed. The results seem to be some important extensions about delayed switching signals from constant delay of discrete‐time systems 34,35 to time‐varying delay of continuous‐time systems; (2) A new auxiliary model about delayed MJSs is developed to overcome the difficulties, such as clear description of so many pair combinations, and assumption on lower bound of dwell time of switched systems 36 to be removed.…”

“…Due to MJSs with Markovian switchings, a special delay exists in MJSs and deeply depends on its mode or switching, which is usually named to be mode‐dependent delay. By applying a Lyapunov function only depending on the current state, the th moment stability of stochastic MJSs was researched in Reference 21. Because of no delay information involved, the obtained results were delay‐independent.…”

“…Since time delay in a system is inevitable, MJS with time delay has received wide-ranging attention. Many important results about delayed MJSs have been obtained, for example, stability, [15][16][17][18][19][20][21] stabilization, [22][23][24][25] H ∞ control and filtering, [26][27][28][29] sliding mode control 30,31 and so forth.…”