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Regularization of Descriptor Systems by Derivative and Proportional State Feedback

Bunse-Gerstner, A., Mehrmann, V. and Nichols, N. (1992) Regularization of Descriptor Systems by Derivative and Proportional State Feedback. Siam Journal on Matrix Analysis and Applications, 13 (1). pp. 46-67. ISSN 0895-4798

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To link to this article DOI: 10.1137/0613007

Abstract/Summary

For linear multivariable time-invariant continuous or discrete-time singular systems it is customary to use a proportional feedback control in order to achieve a desired closed loop behaviour. Derivative feedback is rarely considered. This paper examines how derivative feedback in descriptor systems can be used to alter the structure of the system pencil under various controllability conditions. It is shown that derivative and proportional feedback controls can be constructed such that the closed loop system has a given form and is also regular and has index at most 1. This property ensures the solvability of the resulting system of dynamic-algebraic equations. The construction procedures used to establish the theory are based only on orthogonal matrix decompositions and can therefore be implemented in a numerically stable way. The problem of pole placement with derivative feedback alone and in combination with proportional state feedback is also investigated. A computational algorithm for improving the “conditioning” of the regularized closed loop system is derived.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Meteorology
Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
ID Code:27519
Uncontrolled Keywords:differential-algebraic systems, singular systems, controllability, regularizability, numerical stability, optimal conditioning

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