Stability,Stabilization And H? Control Of Stochastic Systems With Multiplicative Noise

Since the foundation of G.Zames,H?control has become one of the most popular research fields of control theory and a very important robust control method.Its applications in the project have also achieved great success,such as robot control,radar technology and gene network regulation design.The aim of H?control is that,in the presence of the external interference,the designed controller can effectively restrain the external interference to a certain level.H?control requires less information about the external disturbance.It is only assumed that the energy is bounded.So H?filtering has more extensive application value.Firstly,this paper defines uniform detectability of discrete-time stochastic systems with multiplicative noise.Based on uniform detectability,Lyapunov-type theorems associated with generalized Lyapunov equations and exponential stability in mean square sense are presented.Secondly,this paper introducesexact observability and~?exact observability of linear discrete time-varying stochastic systems,which generalizes exact observability of linear time-invariant stochastic systems.A Lyapunov-type theorem is given for discrete periodic systems underexact observability.Thirdly,this paper studies the state feedback stabilizability of a class of nonlinear stochastic systems with state and control dependent noise.Some sufficient conditions on local and global state feedback stabilizations are given in linear matrix inequalities and generalized algebraic Riccati equations.Finally,this paper studies robust stability,stabilization,and H?control for a class of nonlinear discrete time stochastic systems.Firstly,the easily testing criteria for stochastic stability and stochastic stabilizability are obtained via linear matrix inequalities.Then a robust H?state feedback controller is designed such that the concerned system is not only internally stochastically stabilizable but also satisfies a robust H?performance.