Finite-time Stability And Robust Stabilization For Stochastic Systems

In practical engineering applications,the input/output and the state of a system are usu-ally disturbed by many uncertain factors so that they cannot be directly described by ordinary differential equations.Such systems with random factors are called stochastic systems that are described by stochastic differential equations.The universality and complexity of stochastic systems make related research important in both engineering and academic problems.Stabil-ity and robust stabilization are always the primary content of the study on stochastic control systems.Stability is a prerequisite for maintaining the normal work of a system.In previous studies,more attention was paid to the stability of stochastic systems in infinite time interval,such as Lyapunov asymptotic stability.However,the infinite-time stability cannot guarantee that the instantaneous state of the system is always limited to a specific range and often suf-fer from some intrinsic problems.In addition,some systems only need the stable performance within a short time interval,such as the rocket launch.By contrast,the finite-time stability,which directly determines the transient state of system in a limited time interval,seems to be more useful in solving the practical engineering problems,and has been widely used in many fields such as aircraft control.Therefore,the discussion about the finite-time stability of stochas-tic systems in this work is very significant to both theoretical study and practical applications.In modern control theory,the robust control method?robust stabilization?can make the system maintain certain basic performance in the presence of uncertain parameters and disturbances.Therefore,in systems that require high stability and reliability,robust stabilization has attracted much attention as a basic control method guaranteeing the safe operation of the system.Hybrid presented robust control of the system that is stable in a finite time interval is more powerful to solve practical engineering problems.Here,considering both the finite-time stability problem on the finite-time robust control of stochastic systems as follows:1)The finite-time H₂/H_?control of linear stochastic systems is studied.For general the corresponding closed-loop system finite-time stable and finite-time bounded.2)The finite-time H₂/H_?control of linear stochastic systems with?x,u,v?dependent noise is studied.In view of the fact that the actual system state is not completely available,an ?x,u,v?dependent noise.3)The finite-time H₂/H_?control of linear stochastic systems with Wiener and Pois-son interference is studied.For linear stochastic systems with Wiener and Poisson interfer-controller are designed respectively.In terms of methods,the solution problem of finite-time equality)system,which can be conveniently solved by Matlab.Finally,the feasibility and effectiveness of the presented control scheme are positively verified by conducting numerical simulations.