Control Of Semi-Markov Jump Singular Fuzzy Systems With Fractional Brownian Motion

Stochastic system,linear system and generalized system are common types of complex control system models in actual industrial production,because these types of complex control system models can comply with the rapid development of science and technology and industrial revolution,and improve the precision requirements of actual industrial production for the modeling of control system.At present,stochastic systems,linear systems,generalized systems and other control theory research in the development and maturity.In addition,fractional Brownian motion,as a kind of random disturbance input noise in dynamic system,has attracted more and more attention from scholars.At present,the control theory of fractional Brownian motion driven semi-Markov jump fuzzy system is still an open problem to be solved.Based on this,this paper studies some incomplete control theories for fractional Brownian motion driven semi-Markov jump fuzzy systems,fractional Brownian motion driven random generalized systems and fuzzy linear systems,including sliding mode controller and example simulation,state observer and example simulation.The research contents of this paper are as follows:(1)the sliding mode controller design of fractional Brownian motion driven semi-Markov jump fuzzy system is studied.Firstly,a model of semi-Markov jump fuzzy system with fractional Brownian motion is given.Secondly,the sliding mode surface and the sliding mode controller are designed.Then,a sufficient condition for the stochastic admissibility of the system is given by using Lyapunov stability method,and the finite time reachability of the sliding surface of the system is proved.Finally,numerical examples are given to illustrate the feasibility of the sliding mode control method.(2)The sliding mode observer design of fractional Brownian motion driven semi-Markov jump fuzzy system is studied.Firstly,a state observer design for a semi-Markov jump system with fractional Brownian motion is presented.Secondly,the sliding mode surface and controller based on observer are designed.Then,a sufficient condition for the stochastic admissibility of the system is given by using the Lyapunov stability method,and the finite time reachability of the sliding surface of the system based on the observer is proved.Finally,a numerical example is given to illustrate the feasibility of the observer design and sliding mode control method.(3)The admissibility and stability of generalized semi-Markov jump fuzzy systems with fractional Brownian motion are studied.Firstly,the system model and some definitions and lemmas used are given.Secondly,some sufficient conditions for the stochastic admissibility and stability of the system under consideration are given by using linear matrix inequalities.Finally,it is verified by example simulation.