Stability Analysis And Control Of Time-delay Hybrid Systems With Fractional Brownian Motion

Stochastic systems,linear systems and singular systems are common complex control system models in actual industrial production,because these complex control system models can comply with the rapid development of science and technology and industrial revolution,and can improve the accuracy of control system modeling in actual industrial production.At present,the control theories about stochastic systems,nonlinear systems and singular systems control theory are developed and matured right now.In addition,fractional Brownian motion,as an input noise of a class of random disturbances in dynamical systems,has attracted more and more attention.At present,the control theory of stochastic singular systems driven by fractional Brownian motion is still an open problem to be solved.Based on this,this paper studies some incomplete control theory problems of fractional Brownian move-driven Markov hopping singular systems,fractional Brownian move-driven stochastic singular systems and fuzzy linear systems,including quantization controller and case application,sliding mode controller and case application,state observer and case application,etc.The research contents of the specific chapters of this paper are as follows:(1)In this paper,the problem of the quantized feedback control is considered for a class of uncertain time-delay Markov jump singular systems driven by fractional Brownian motions.Firstly,the control signal of the model is quantized by uniform operator.The quantized input signal is composed of two parts,one is the linear control that deals with the uncertainty of the model,the other is the nonlinear control that deals with the error of the quantizer.Secondly,by introducing the matrix inequality condition,the stochastic admissibility criterion of the system with quantized state feedback controller is obtained.Finally,a simulation example is given to illustrate the feasibility of the design of the quantified feedback controller.(2)In this paper,the sliding mode observer design of uncertain delay singular systems driven by fractional Brownian motion is studied.Firstly,the design of state observer for uncertain delay singular systems with fractional Brownian motion is given.Secondly,a sliding mode surface and a sliding mode controller based on observer are designed.Then,sufficient conditions for the stochastic admissibility of the system are given by 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 observer design and sliding mode control.(3)The problem of the fuzzy H_? state feedback control for a class of uncertain linear systems with fractional Brownian motions and multiple state delays is addressed in this paper.First,Takagi-Sugeno(T-S)model with time delay and uncertain parameters is used to model the linear system.Secondly,the design of fuzzy H_? robust controller is given.Then the Lyapunov stability method and fractional infinitesimal operator is used to determine H_? stability in the form of linear matrix inequality(LMIs).Finally,a numerical example is given to illustrate the feasibility of fuzzy H_? robust controller design.