Study On Some Problems Of Stability And Stabilization For Discontinuous Dynamical Systems

The thesis can be mainly divided into following parts. The stability analysis for the piecewise continuous systems, including input-to-state stability and output-to-state stability. Exponential stability analysis for nonlinear switching systems on bounded regions. Feedback stabilization for several classes of nonlinear systems.Firstly,the input-to-state stability(ISS) problems are considered for the piecewise continuous systems. The time-delays,impulsive and disturbances are considered for the piecewise continuous systems. In this case,stability conditions are obtained. ISS,iISS(Integral input-to-state stability),IOSS (Input-output-to-state stability)and IIOSS(Integral input-output-to state stability)-type theorems are obtained.Secondly,exponential stability for nonlinear switching systems on bounded regions is studied.Switching systems are discontinuous system,factually. The exponential stability conditions for switching systems,the Frechet differentiable operators in Hilbert space and discrete T-S fuzzy systems on bounded regions are studied. Resort to new Lipschtiz constants,the exponential stability for these systems are obtained.Thirdly,stability and stabilization for the multi-agent systems are considered. For-mation in flocking without leaders is studied. Lyapunov-Razumikhin theorem is applied in the formation problem. Formation aims can be realized through designing suitable formation algorithms.Finally,the quantized feedback stabilization problems are studied.First,the quan-tized feedback problems with static quantizers for the piecewise affine systems are studied with the help of Lyapunov-Razumikhin theorem and Lyapunov-Krasovskii theorem.How to design suitable quantized feedbacks to realize ISS for the piece-wise continuous systems is studied.On the other hand,the dynamic quantizers are constructed to discuss quantized feedback stabilization of one class of nonlinear dy- namical systems.