Stability robustness of linear discrete time systems

This dissertation is intended to develop stability robustness bounds for linear time-invariant discrete systems. The problem of maintaining the stability of a nominally stable system subjected to perturbation has been an active area of research for some time. Some of the existing time-domain controller design methods for discrete-time systems are applicable to "matched" uncertain systems. Other controller design methods follow the approach of establishing bounds on allowable perturbations, and then using theses bounds to select feedback controllers, such as LQ regulators. However, these controller design methods do not directly consider the stability robustness aspect in the design itself. To improve stability robustness bounds, this dissertation proposed a control design method that includes a stability robustness component in the design procedure for some optimal topics. The stability robustness component is based on a recently developed unstructured perturbation bound for time-varying perturbations that used Lyapunov theory and singular value analysis. The form of the controller considered in this dissertation is a reduced-order linear dynamic compensator which operates on the available outputs. The controller design for optimal topics is developed by the parameter optimization technique and involving the solution of five algebraic matrix function, four of which are discrete-time Lyapunov matrix functions. Some results show that the controller design with stability robustness component obtains better bounds than traditional one.