Analysis And Design Of IT2 Nonhomogeneous Markovian Jump Stochastic Singular Systems

As one of the effective tools to approximate complex nonlinear systems,T-S fuzzy model has been promoting the continuous research and development of nonlinear systems since it was proposed in 1985.Compared with the type-1 T-S fuzzy model,the type-2 T-S fuzzy model can better represent and deal with the uncertainty of the system,but the disadvantages is that it increases the computational burden of the system.As a special case of the type-2 fuzzy model,the interval type-2 fuzzy model not only retains the advantages of the type-2 fuzzy model,but also reduces the computational complexity.Based on the interval type-2 T-S fuzzy model,this paper focuses on continuous-time and discrete-time stochastic singular non-homogeneous Markovian jump systems to study system regular,impulse-free(causal),stochastic stability and controller design.The research content of this article is mainly divided into the following three parts:Part Ⅰ:The problem of admissibility and stabilization for a class of interval type-2 stochas-tic singular non-homogeneous Markovian jump systems is studied.The time-varying property of the transition rates is considered to be finite piecewise homogeneous.Firstly,construct the stochastic Lyapunov function,based on the generalized It(?) formula and the inequality scaling technique,the sufficient condition is established for the stochastic admissibility of the system.Secondly,in the process of designing the state feedback fuzzy controller,The introduction of control gain will lead to the generation of nonlinear matrix inequalities.By introducing the linear transformation composed of specific matrix variables,the nonlinear matrix inequalities are transformed into linear matrix inequalities.Finally,a numerical simulation example verifies the effectiveness of the method.Part Ⅱ:The problem of observer-based controller design for interval type-2 non-homogeneous Markovian jump stochastic descriptor systems is investigated.Based on the stochastic Lyapunov theory and Dykin formula,the sufficient condition for the stochastic ad-missibility of the closed-loop error system is established.Different from the general system,it is difficult to separate the observer gain and the controller gain at the same time due to the existence of the brown parameter.By introducing some new variables,the nonlinear matrix inequalities are transformed into equivalent form,so that the control gain of the system and the observer gain can be separated,and the problem of observer and controller design can be solved.The feasibility of the proposed method is further verified by numerical simulation.Part Ⅲ:The H_∞control problem for a class of interval type-2 discrete stochastic singular systems with non-homogeneous Markovian jumps is studied.The non-homogeneous characteristics of the system can be represented by a high-order Markovian process.Based on the stochastic Lyapunov function,slack variables are introduced,and sufficient conditions for system regular,causal and stochastic stability are obtained.In the design of the controller,By using a augmented system method,a sufficient condition for the closed-loop system to satisfy the H_∞performance index is given.Numerical simulation illustrates the practicability of the proposed method.