Unified approach for singularly perturbed control systems.

摘要

The theory of singular perturbation has been a highly recognized and rapidly developing area of control systems in the last thirty years. Results now exists for both the continuous-time and discrete-time systems. However, in the way that these results are normally presented, the solutions to the discrete-time and continuous-time cases evolve from different starting points and seem to bear no relationship to each other.; The aim of this dissertation is to develop a unified framework for discrete-time and continuous-time singularly perturbed systems. The discrete-time singularly perturbed control systems results are reorganized so that they are compatible in a way that the continuous-time singularly perturbed control system results are normally presented. This is, in part, achieved by using a newly developed “Unified Approach” to digital system theory, first proposed by Middleton and Goodwin.; We first formulate the problem by modeling the singular perturbation parameter from the standpoint of the state space formulation and the second order unified equation. Building upon these results, we further apply this technique to state-feedback, robust state-feedback, Linear Quadratic Regulator (LQR) and $H\infty$ optimization control problems. The unified results developed in this Dissertation are valid for both the continuous-time case (sampling interval T = 0) and the discrete-time (sampling interval T > 0).