Finite-Time Observer-Based Sliding-Mode Control for Markovian Jump Systems With Switching Chain: Average Dwell-Time Method
针对具有确定性切换链、时变时延和丢包的随机马尔可夫跳变系统，设计了非脆弱有限时间有界滑模观测器，并提出了基于观测器的滑模控制方法，保证系统在有限时间内的有界性。
In this article, the finite-time observer-based sliding-mode control (SMC) problem is considered for stochastic Markovian jump systems (MJSs) with a deterministic switching chain (DSC) subject to time-varying delay and packet losses (PLs). First, the stochastic MJSs with DSC are appropriately modeled and the PLs case is characterized by using some Bernoulli random variables. Then, a nonfragile finite-time bounded sliding-mode observer is designed. Our objective is to propose a finite-time observer-based SMC approach such that for the above addressed system, the finite-time boundedness in a certain time interval can be guaranteed by giving sufficient criteria via the stochastic analysis skills and average dwell time (ADT) method. Moreover, a new robust finite-time sliding-mode controller can be designed to ensure reachability of the common sliding surface in the estimation space. Finally, a numerical example is provided to illustrate our theoretical results.