Simultaneous Stabilization And Simultaneous H~∞ Control For Uncertain Nonlinear Systems

This paper is mainly to design a unified continuous state feedback controller that stabilizes a class of uncertain nonlinear system or simultaneously stabilizes a collection of uncertain nonlinear systems.First of all,the problems of single input nonlinear system. Continuous feedback con-troller is constructed using control Lyapunov function method and Arstein Theorem.A necessary and sufficient conditions for the existence of continuous feedback controller that stabilizes single input nonlinear system.The example is illustrated the validity of the the-orem.The result extends the existing one for multi-input nonlinear system.Secondly, the problems of robust stabilization for uncertain nonlinear systems.We give a sufficient condition of the existence of and feedback controllers for the uncertain nonlinear systems and a universal formula for feedback controllers. By using state space method obtained a sufficient conditions of the existence of feedback controller for a family of uncertain nonlinear systems, and also obtained a universal formula for simultaneous stabilization controllers.Finally, the problems of simultaneous H∞control for a group of uncertain nonlinear systems.Introducing The concept of control storage function (CSF) and L2—gain small control property, and obtained a sufficient conditions of the existence of H∞control and also obtained a universal formula for simultaneous H∞stabilization controllers for a group of uncertain nonlinear systems.