Regularization of descriptor systems

Nichols, N. K. ORCID: https://orcid.org/0000-0003-1133-5220 and Chu, D. (2015) Regularization of descriptor systems. In: Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory. Springer International Publishing, Switzerland, pp. 415-433. ISBN 9783319152592 doi: 10.1007/978-3-319-15260-8_15

Abstract/Summary

Implicit dynamic-algebraic equations, known in control theory as descriptor systems, arise naturally in many applications. Such systems may not be regular (often referred to as singular). In that case the equations may not have unique solutions for consistent initial conditions and arbitrary inputs and the system may not be controllable or observable. Many control systems can be regularized by proportional and/or derivative feedback.We present an overview of mathematical theory and numerical techniques for regularizing descriptor systems using feedback controls. The aim is to provide stable numerical techniques for analyzing and constructing regular control and state estimation systems and for ensuring that these systems are robust. State and output feedback designs for regularizing linear time-invariant systems are described, including methods for disturbance decoupling and mixed output problems. Extensions of these techniques to time-varying linear and nonlinear systems are discussed in the final section.