Observer Based Finite-Time Stabilization for Discrete-Time Markov Jump Systems with Gaussian Transition Probabilities

Robust finite‐time H ∞ control for switched systems by using sojourn‐probability‐dependent method

“…Definition 1 [13] (stochastic FTB): A discrete-time switched system (11)-(13) is said to be stochastic FTB with respect to given (c 1 ,…”

“…Recently, there are many research achievements on the finite-time control problem [11][12][13][14][15][16][17][18][19][20]. In [12], the authors deal with finite-time stochastic stability for a class of discrete linear systems by using asynchronous switching.…”

“…However, up to now, the switching rules which have significant impact on the system performance are controlled switching, arbitrary switching, dwell-time switching and Markov process switching. Among them, Markovian jump systems, where the switching between the subsystems is governed by a Markov process, have attracted considerable attentions [10,[13][14][15][21][22][23]. For instance, work [13] mainly solves the observer-based finite-time stabilisation problem for discrete-time Markov jump systems, and work [14] combines Markovian jump systems with networks and analyses the finite-time global synchronisation of the new model.…”

Observer‐based finite‐time stabilization for discrete‐time switched singular systems with quadratically inner‐bounded nonlinearities

“…On the other hand, in many practical systems, the state variable should be less than a certain bound during a fixed time interval, such as asynchronous transfer mode network control and aircraft control; hence, finite‐time stability is useful in these cases . In recent years, finite‐time stability and stabilization and H ∞ finite‐time control problems have been widely investigated . For example, Lin et al discussed finite‐time boundedness and L 2 ‐gain analysis for switched delay systems and switched systems with ADT, respectively.…”

“…Muoi et al discussed the finite‐time stabilization problem for singular linear discrete delay systems. On the basis of the observer, finite‐time stabilization for discrete‐time Markov jump systems with Gaussian probability was considered in the work of Chen et al, and the observer‐based controller was provided by using LMIs with an equation constraint. However, so far, the issue of finite‐time control for switched singular systems with quadratically inner‐bounded nonlinearities has not been addressed, which motivates our research.…”