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Output feedback in descriptor systems. (English) Zbl 0812.93034

Dooren, Paul Van (ed.) et al., Linear algebra for control theory. Based on the proceedings of a workshop which was an integral part of the 1991-92 IMA program on “Applied Linear Algebra”, Minneapolis, MN (USA). New York, NY: Springer-Verlag. IMA Vol. Math. Appl. 62, 43-53 (1994).
Summary: A summary is given of conditions under which a descriptor, or generalized state-space system can be regularized by output feedback. Theorems are presented showing that under these conditions proportional and derivative output feedback controls can be constructed such that the closed loop system is regular and has index at most one. This property ensures the solvability of the resulting system of dynamic-algebraic equations. A canonical form is given that allows the system properties as well as the feedback to be determined. 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. A computational algorithm for improving the ‘conditioning’ of the regularized closed loop system is described.
For the entire collection see [Zbl 0793.00032].

MSC:

93B52 Feedback control
93C05 Linear systems in control theory
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