Research On Robust Control Of Hybrid Systems With Input Constraints

Hybrid systems are a class of systems combining continuous dynamics with discrete dynamics.As a special hybrid system,the hybrid impulsive system depending on time switching has been applied in biomedicine,economics,ecology and control disciplines.Due to the complex dynamics,control input constraints,model uncertainty and exter-nal disturbances,it brings difficulties and challenges to the research of hybrid impulsive systems.In this paper,based on the existing research results and methods,the stability,switching control and robustH_?control of hybrid impulsive systems are studied.The main results are summarized as follows:(1)For the hybrid impulsive systems with input constraints,a switching control s-trategy is designed to stabilize the impulsive systems.The input constraints considered are novel reverse polytopic constraints which can avoid a series of special values.Based on Lyapunov stability theory,the matrix inequality conditions for the closed-loop systems stability and the design method of controller gain are established.The stability criterion is given by linear matrix inequality when applying state feedback control;the stability criterion is given by bilinear matrix inequality when applying output feedback control.(2)For uncertain hybrid impulsive systems with input constraints,the robust stabil-ity and robustH_?control are studied.The robust control problem of hybrid impulsive systems is extremely challenging when there exit parameter uncertainties and external disturbances.When the external disturbances are not considered,the hybrid switching controller is designed,sufficient conditions for robust stabilization of the hybrid impulse system are established,and the input constraint of the controller is ensured.when con-sidering the external disturbance,the robustH_?control of the system is further studied.(3)For uncertain hybrid impulsive systems with input constraints,less conservative conditions of robust stability and robustH_?control are established.By introducing a control parameter into the previous research results,the proposed less conservative condi-tions can be applied to both stable and unstable jump dynamics of the hybrid impulsive systems.