Robust Control For Classes Of Switched Linear Systems

This dissertation studies robust control problem for classes of switched linear systems, focusing on the problems of robust quadratic stability, robust H_∞ control and guaranteed cost control. The main results are summarized as follows.The problem for robust quadratic stability of switched linear systems with uncertainties of convex cone is discussed. The uncertainties form a convex cone spanned by a number of constant known matrixes. By using the convex combination method, quadratic stability conditions are derived for continuous switched linear systems and discrete switched linear systems, respectively. Only the matrixes of extreme points are involved in the conditions. The associated switching laws are also designed.By using the concept of completeness, a necessary and sufficient condition that guarantees quadratic stability is given for switched linear systems with polytopic perturbations. With single-Lyapunov function method and multiple-Lyapunov function method, sufficient conditions for quadratic stability are given with switching laws constructed.An interval matrix is introduced to transform a switched linear system into an interval system. A sufficient condition for quadratic stability of switched linear systems under arbitrary switching laws is presented in terms of linear matrix inequality. This condition implies the existence of a common quadratic Lyapunov function for all subsystems. While this condition is much simpler than usual conditions for the existence of a common quadratic Lyapunov function because only one linear matrix inequality needs to be solved while a number of linear matrix inequalities are involved in usual common quadratic Lyapunov function method. This is even more obvious when the number of subsystems is large.The quadratic robust stability problem for a class of switched linear systems and these systems with certain nonlinear perturbations under arbitrary switching laws is investigated. Sufficient conditions for quadratic robust stability are established by Riccati inequalities respectively for switched linear systems with time-variant perturbations and certain nonlinear perturbations under arbitrary switching laws.The problem of H_∞, robust control for uncertain switched linear systems under...