This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state variable, and addressed the problem of stochastic stability and stabilization analysis for the proposed system. Numerically solvable sufficient conditions for the stochastic stability and stabilization of the proposed system is established in terms of linear matrix inequalities. The obtained results are illustrated in numerical examples.
Robust Decentralized Stabilization of Markovian Jump Large-Scale Systems: A Neighboring Mode Dependent Control Approach
University of Science and Technology of China（中国科学技术大学）；University of New South Wales at the Australian Defence Force Academy（澳大利亚国防军学院新南威尔士大学工程学院与信息技术学院）
In this paper, we study the stabilization of two interdependent Markov jump linear systems (MJLSs) with partial information, where the interdependency arises as the transition of the mode of one system depends on the states of the other system. First, we formulate a framework for the two interdependent MJLSs to capture the interactions between various entities in the system, where the modes of the system cannot be observed directly. Instead, a signal which contains information of the modes can be obtained. Then, depending on the scope of the available system state information (global or local)…
This paper discusses the stability analysis of linear parameter varying systems with a parameter-dependent delay where the parameters are assumed to be stochastic piecewise constants under spontaneous Poissonian jumps. Based on stochastic Lyapunov-Krasovskii functionals, we also provide sufficient synthesis conditions for the gain-scheduled state-feedback controller with memory in terms of parameter-dependent linear matrix inequalities (LMIs). Such synthesis conditions are computationally intractable due to the presence of integral terms. However, we show that these LMIs can be equivalently re…
By using dissipativity approach, we establish the stability condition for the feedback connection of a deterministic dynamical system $Σ$ and a stochastic memoryless map $Ψ$. After that, we extend the result to the class of large scale systems in which: $Σ$ consists of many sub-systems; and $Ψ$ consists of many "stochastic actuators" and "probability controllers" that control the actuator's output events. We will demonstrate the proposed approach by showing the design procedures to globally stabilize the manufacturing systems while locally balance the stock levels in any production process.
This paper proposes a line integral Lyapunov function approach to stability analysis and stabilization for Itô stochastic T-S models. Unlike the deterministic case, stability analysis of this model needs the information of Hessian matrix of the line integral Lyapunov function which is related to partial derivatives of the basis functions. By introducing a new method to handle these partial derivatives and using the property of state-dependent matrix with rank one, the stability conditions of the underlying system can be established via a line integral Lyapunov function. These conditions obtain…
