Robustness Analysis of Linear Control Systems with Uncertain Parameters by the Method of Convex Decomposition

Abstract

This paper begins with a brief summary of the method of convex decomposition, which was first proposed by Kiendl [1, 2] in 1984 and then subsequently developed in cooperation with Ossadnik [3 to 9]. The computer-based method serves as a tool for the robustness analysis of continuous or discrete time linear systems in a state-space representation with uncertain constant or time-varying parameters. For proof of stability purposes, a box-shaped uncertainty domain P is decomposed into ever decreasing sub-boxes until a stability establishing Lyapunov function has been found for each subbox. Exemplified by a case study, it will be demonstrated that the combinatorial explosion can be heavily restrained by strategy elements which have been developed in the meantime. As a result, the method’s practical areas of application may be widely expanded. A fundamental — mathematically obvious but not yet put into practice — extension of the method of convex decomposition is presented in the appendix. It enables broad classes of nonlinearly parameter dependent system matrices to be analysed in the same simple manner as linearly parameter dependent system matrices — without circuitous detours.