Regularization of Descriptor Systems

Nancy K. Nichols () and Delin Chu ()
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Nancy K. Nichols: University of Reading, Department of Mathematics
Delin Chu: National University of Singapore, Department of Mathematics

Chapter Chapter 15 in Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory, 2015, pp 415-433 from Springer

Abstract: Abstract 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.

Keywords: Derivative Feedback; Regular Descriptor System; System Pencil; State Feedback Problem; Feedback Matrices (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-15260-8_15

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DOI: 10.1007/978-3-319-15260-8_15

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