New approach on solving control problems with descriptor systems

Abstract

Control problems for plants that are described with models employing descriptor or singular linear systems was an intensive research area in the past. Still it is an open and interesting research topic due to issues of efficient solving differential equations under algebraic constraints. This paper presents a new practical and/or applicable solution to the output feedback control problems with controlled and measurement outputs by using descriptor generalized plant (GP) representation. It is derived through an appropriate transformation into control problem with a state-space GP. This new approach yielded a method of finding optimal controllers for descriptor GPs that simplifies all the existing methods. In addition, relevant regularity conditions for descriptor GP are defined and necessary and sufficient conditions are derived, which are expressed in terms of the given data matrices. In turn, it is proven that the original descriptor GP is regular, if and only if the state-space GP, obtained by a static output feedback (SOF), is regular. The third paper’s result is a H∞ controller design with more robust properties with respect to the existing H∞ controllers and of reduced order. The controller is obtained by solving a SOF problem and a two-block problem. Several numerical examples are given within the main sections in order to clarify the novel results of this paper.