Analysis And Controller Design For T-S Fuzzy Markov Jump Systems With Saturation Constraints

Markov jump system is usually used to describe the structure of system by the randomness of the sudden changes,which often comes from the system components or connections between components of sudden failure.It also comes from sudden environmental changes and the change of nonlinear system working point and so on.For nonlinear jumping system,the problem of describing difficulty can be overcome with T-S fuzzy model,and the conclusion of linear systems can be popularized.After analyzing and summarizing the research background and existing conclusions of the subject,we study the system model,performance index and feedback control signal from different aspects.Based on the Markov jump system of T-S fuzzy model,the paper considers the influence of input saturation constraint and time-varying delay.Then analysis is conducted on stability of the system base on LMI technology.And the corresponding feedback controller is designed.Based on two kinds of stability theory,three kinds of performance indicators and three kinds of feedback controller design methods are presented here.The main work of this academic paper includes the following aspects:(1)With input saturation constraint and time-varying delay of T-S fuzzy Markov jump system,discussing the control problem of certain and uncertain in jump transition probability.On the one hand,when the jump transition probability is partially unknown but bounded,presenting a closed-loop system stochastic stable in the Lyapunov stability theory and criterion with H_?performance indicators,then the state feefback controller design of the system is given by matrix equivalent transformation.On the other hand,considering the disturbance input in the control output of the system model,the proper Lyapunov functional has been selected,the sufficient conditions of stochastic stability of the closed loop system.is obtained,with the aid of Wirtinger integral inequality and Free weight matrix,the delay-dependent criteria reduce the conservatism,under the theory of passive,the gain of the corresponding state feedback controller is given.,At last,the feasibility verification is carried out by simulation,the estimation of saturation attraction is given.based on the optimization problem of LMI.(2)We discuss the non-fragile output feedback control problem of a kind of uncertain saturated T-S fuzzy Markov jump time-delay system in this paper.The sufficient conditions of the closed-loop system in the stability theory of stochastic stability and dissipative properties are given.Considering that the system state cannot be fully known,the output feedback control is carried out.Considering parameter small deviation,there is uncertainty when constructing controller.,the non-fragile dissipative output feedback controller is obtained.Based on LMI technology,the estimation of saturated attraction domain is obtained,which is verified by simulation.Numerical simulation shows that the proposed method has better conservatism compared with the existing results.According to the actual single arm manipulator,the T-S fuzzy Markov jump system is modeled.The feedback control law is obtained by simulation,and the system state response curve is obtained.The system tends to zero equilibrium point and is random stable.(3)Based on the finite time stability theory,the design of the state feedback controller for the generalized T-S fuzzy Markov jump system with input saturation and time-delay is studied.This paper also focuses on transient performance,considering finite time stability and control problems under the algebraic constraint of saturated T-S fuzzy Markov jump time-delay system.The sufficient conditions for regular,no pulse and stability for the system are given in this paper,and the memory state feedback controller with time delay is designed.A numerical example is given to verify the effectiveness of the proposed method.(4)Based on the finite time stability theory,the design of the dissipative output feedback controller for the generalized T-S fuzzy Markov jump system with input saturation is studied.For the unknown situation of the jump transfer probability matrix,the paper gives the criterion of the finite time bounded and dissipative of the closed loop system,and the output feedback controller is designed.Finally,numerical examples are used to verify the validity of this conclusion.At the same time,the estimation of the maximum attraction domain of the system is obtained.