New results on stability of singular stochastic Markov jump systems with state-dependent noise

Abstract

SUMMARYThis paper aims to develop the stability theory for singular stochastic Markov jump systems with statedependent noise, including both continuous-time and discrete-time cases. The sufficient conditions for the existence and uniqueness of a solution to the system equation are provided. Some new and fundamental concepts such as non-impulsiveness and mean square admissibility are introduced, which are different from those of other existing works. By making use of the H-representation technique and the pseudo inverse E C of a singular matrix E, sufficient conditions ensuring the system to be mean square admissible are established in terms of strict linear matrix inequalities, which can be regarded as extensions of the corresponding results of deterministic singular systems and normal stochastic systems. Practical examples are given to demonstrate the effectiveness of the proposed approaches.

Asymptotic stability in probability of singular stochastic systems with Markovian switchings

“…Remark Mean‐square stability of singular stochastic systems was studied in . Indeed, asymptotic stability in probability is different from conventional mean‐square stability.…”

“…Example Consider the dynamic Leontief model of a multi‐sector economy without final demands where x k is the levels of production, G is the Leontief input–output matrix, and E is the capital coefficient matrix. In multi‐sector economic systems, both G and E have nonnegative elements.…”

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

“…One difficulty is that the controller gain matrix can not be easily obtained by pre-and post-multiplying the inverse of Lyaunov matrix P(r t ) since the obtained condition can not be linearized, this question motivates us to avoid the traditional method and turn to the prospect of new gain matrices in controllers. In addition, different from [20], it can be found the derivative of operator (⋅) for singular stochastic MJSs is not directly obtained by using the general Itô formula, new proof method with assumption on matrices in the diffusion part is proposed in this note. Therefore, in this paper, we are devoted to investigating the stochastic stability and stabilization of singular Itô-type stochastic Makovian jump systems.…”

“…A detailed proof about the non-impulse, uniqueness of solution and asymptotic stability for singular stochastic MJSs is given in Theorem 1. The condition (20) in some other papers is also referred to as exponential stability in mean square sense. Now, for computation purpose, the conditions (9) and (10) need to be unified into a single strict LMI which can be solved by Matlab toolbox.…”

Finite-time event-triggered control and fault detection for singular Markovian jump mixed delay systems under asynchronous switching

“…Different from other regular systems, singular systems are more general and complex owing to not only the stability are need to be considered, but also regularity and absence of impulses or causality is need to be considered. Due to this fact singular systems can better describe and analyze the behavior of some physical systems than regular ones by standard state-space systems [28,29]. Moreover, since the existence of time-delays often causes undesirable behavior such as degradation stability in dynamical systems, one of the major issues of stability and control analysis for time-delay singular systems has been studied extensively in actual problems [30,31].…”