A Class Of Nonlinear Switched Systems Analysis And Control

A switched system is a class of hybrid system composed of several dynamical subsystems and a switching law that specifies the active subsystem at each instant of time. Switched systems arise in many engineering applications, for example, in motor engine control, robotics control, and networked control systems, etc. It is of great practical value and theoretical significance to investigate switched systems. This thesis concerns with some issues related to the stability analysis, control design and observer design of switched nonlinear systems. The main contributions are summarized as follows:(1) Sufficient conditions are derived to guarantee stability or boundness of switched nonlinear systems' solution. When the system is composed of unstable subsystems and stable subsystems, it has been proven that if the switching law satisfies some conditions, then stability or boundness is guaranteed.(2) The dynamical dwell time approach is proposed. The dwell time of each switching instant can be estimated by this approach which shows less conservative in switching law design than dwell time approach. Then the proposed approach is extended to the switched nonlinear systems with both stable and unstable subsystems.(3) Control Lyapunov function approach is used to stabilize the switched nonlinear systems with the pre-specified average dwell time. If there are disturbances, the controller designed by control Lyapunov function approach guarantees the input-state stability of the switched nonlinear systems to disturbances.(4) Using dynamical dwell time approach the controllers designed by control Lyapunov function approach can stabilize the switched nonlinear systems with the pre-specified switching sequence. Then the proposed approach is extended to the switched nonlinear systems composed of both stabilizable and unstabilizable subsystems.(5) Back stepping method is applied to design the state feedback controllers for switched nonlinear systems whose switching law designed by Multi-Lyapunov functions. Then the proposed approach is extended to systems with uncertainties.(6) A sufficient and necessary condition for the solvability of output and disturbance decoupling of single-input single-output switched nonlinear systems with uniform normal norm is presented. Furthermore, a similar sufficient and necessary condition for the solvability of output and disturbance decoupling of switched nonlinear systems is derived when disturbance can be measured and utilized for designing state feedback controller.(7) By solving a set of linear matrix inequalities (LMIs) and updating estimated state, an observer design methodology for a class of switched nonlinear systems is proposed.