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Singular systems: A new approach in the time domain. (English) Zbl 0612.93030
A new approach in the time domain is developed for the study of singular linear systems of the form Eẋ$$=Ax+Bu$$, $$y=Cx$$ with E singular. Central to the approach is the fundamental triple $$((\alpha E-A)^{-1}E,(\alpha E-A)^{-1}B,C)$$ with $$\alpha$$ a real number satisfying det($$\alpha$$ E- A)$$\neq 0$$. Controllability and observability matrices are expressed in terms of the fundamental triple. New tests for impulse controllability and impulse observability are also established. Feedback control problems including pole placement, decoupling, and disturbance localization are studied by use of a modified proportional and derivative feedback of the state in the form of $$u=F(\alpha x-\dot x)+v$$.

##### MSC:
 93C05 Linear systems in control theory 34A99 General theory for ordinary differential equations 93B05 Controllability 93B07 Observability 93B55 Pole and zero placement problems 93D15 Stabilization of systems by feedback
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