Stochastic Stability and Stabilization of Singular It‐type Markovian Jump Systems with Uncertain Transition Rates: An LMI Approach

Abstract

This paper investigates the stochastic stability and stabilization for a class of singular stochastic systems of Itô‐type with Markovian switching, the transition rates (TRs) in the jumping processes are uncertain. The aims are to establish sufficient conditions to ensure the considered system to be stochastically stable in the mean square sense, which is supported by a detailed proof of existence and uniqueness of the system solution, and to propose a controller such that the system can be stabilizable. The controller is first proposed and has advantage over traditional ones, the controller gain matrices are obtained by solving a strict linear matrix inequality (LMI). Finally, a numerical example is provided to illustrate the validity of the obtained methodology.

Finite-Time Stochastic $H_\infty$ Control for Singular Markovian Jump Systems With $(x,v)$ -Dependent Noise and Generally Uncertain Transition Rates

“…In addition, the item (i) of Assumption 3 was given in [3], [4], which is less conservative than previous work such as [1], [2]. Recently, the item (ii) of Assumption 3 was presented in [8]. However, it can be proved that two conditions are equivalent.…”

“…Remark 16: As said in [8], [37], [45], [46], it is difficult to design a convex controller for systems with uncertain TRs or GUTRs. This is because the nonlinear association terms caused by the Young inequality often emerge.…”

Non‐fragile sliding mode control of discrete switched singular systems with time‐varying delays

“…It is universally known that singular systems are capable of describing some physical systems, for instance, networks, robotic systems and economic systems [1–3]. Composed of algebraic equations and differential equations (or difference equations), singular systems are also called as generalised state‐space systems, descriptor systems, semi‐state systems and so on.…”

Stabilization for Markovian Jump Distributed Parameter Systems With Time Delay

“…Through a lot of research work, it is found that these random changes usually follow the law of Markovian jump process. Up to present, many results of Markovian jump systems with timedelay have emerged [37]- [53], such as finite-time stability and stabilization [37], Finite-time H∞ filtering [38], Stability and stabilization [39], Exponential stability [40], and stochastic stability [41]. Due to singular Markovian jump timedelay systems [42] and neutral Markovian jump systems with time-varying delays [43], some scholars have discussed the Exponential stability.…”

“…As we know, it is not easy to obtain all the accurate transition rate in practical application due to huge cost and lack of technology. In [49]- [53], Markovian jump systems with general unknown transition probability matrices have been reported.…”