Stability And H_∞ Control For Classes Of Switched Nonlinear Systems

Switched systems are a class of important hybrid systems which find broad applications. The behavior of switched systems is very complicated because of the interaction between the continuous dynamics and discrete switching signals. This provides new areas of research and challenging problems in information sciences, control sciences and related fields. Meanwhile, research results of switched systems also make significant reference to general hybrid systems in terms of ideas, methods and theories. Therefore, the study of switched systems has great academic value and significant applications.This dissertation studies stability and H_∞, control problems for classes of switched nonlinear systems. Lyapunov function method and differential geometry method are two major methods adopted in the study. Stability analysis and design methods of robust and H_∞ control are presented. The main contributions are as follows.A uniform normal form of switched nonlinear systems is presented, which generalizes the notion of normal form of nonlinear systems to switched systems. A geometric condition for the existence of the uniform normal form and corresponding coordinate transformation are derived. With the help of the uniform normal form, conditions for stabilizability of switched nonlinear systems under arbitrary switching are analyzed.The problem of global quadratic stability of switched nonlinear systems in block-triangular form under arbitrary switching is addressed. Under the assumption that all block-subsystems are zero input-to-state stable, a common Lyapunov function is constructed iteratively by using the Lyapunov functions of block-subsystems. A sufficient condition for the problem to be solvable is presented.Global stabilization of a class of cascade switched nonlinear systems with control input is analyzed. Robust stability of a class of uncertain cascade switched nonlinear systems is also discussed.