H_∞ Norm And Control For Descriptor Symmetric Systems

Symmetric systems are a classe of systems with special structure, which have comprehensive practical application background. In the light of recent work on the theory of symmetric systems, this thesis studties the problems of H_∞norm for generalized symmetric and descriptor symmetric systems, and the H_∞control for the latter systems. The main contents and results in this thesis are as follows:1. As to the generalized symmetric systems, the problem of H_∞norm for two especial cases is concerned. The problem is equivalently converted into corresponding problem of normal symmetric systems via simple algebraic transform, and is resolved by the techniques of normal sysmmetric systems. The explicit expression for H_∞norm of generalized symmetric systems is derived. Accordingly, the corresponding result for linear discrete systems is derived.2. The problem of H_∞norm of descriptor symmetric systems is addressed. The results for normal symmetric systems are generalized to the descriptor symmetric systems by generalized bounded real lemma (GBRL). First, the solutions of GBRL for two especial cases are obtained. And then, the explicit expression for H_∞norm of descriptor symmetric systems is derived.3. The problem of state feedback and dynamic output feedback for descriptor symmetric systems are addressed. The conditions for the existence of state feedback H_∞controller and dynamic output feedback H_∞controller which make the closed loop systems symmetric and admissable are obtained. And then the condition for existence of dynamic symmetric output feedback H_∞controller for descriptor symmetric systems is given.