H_∞ Control For Generalized Linear Systems, Singularly Perturbed Systems And Singular H_∞ Control Problem

H_∞ control has made great progress in disturbance rejection and robust stabilization for uncertain systems and attracted much attention in the past decade. This dissertation discusses three problems concerning H_∞ control:First, H_∞ control for generalized linear systems. A set of necessary and sufficient existence conditions for the problem is derived. Then the structure of the H_∞ sub-optimal controller is analyzed, and a two-stage controller design procedure is proposed.Second, H_∞ control for singularly perturbed linear systems. Parameter-independent existence conditions are obtained, and an H_∞ sub-optimal controller is constructed explicitly. The controller has the property that its slow(fast) part is an H_∞ sub-optimal controller for the slow(fast) subsystem of the original full-order system. Then a design procedure for parameter-independent H_∞ sub-optimal controllers is proposed.Third, singular H_∞ control problem. The existence conditions are derived directly via the perturbation approach. Then the possibility of designing a reduced-order H_∞ controller for the perfect measurement case is addressed.Finally, the theory for singularly perturbed systems is applied to automotive active suspension systems. The resulting reduced-order H_∞ controller can achieve better performance by simulation.The main contribution of the dissertation includes:1. A complete set of necessary and sufficient conditions for the existence of H_∞ controllers for generalized linear systems is derived.2. H_∞ control theory for singularly perturbed systems is generalized to non-standard case.3. Existence conditions for singular H_∞ control problem are derived in a simple method, and the result can be used to construct a reduced-order H_∞ controller for some cases.