## Impulse observability and impulse controllability of linear time-varying singular systems.(English)Zbl 1058.93011

Linear, finite-dimensional, continuous-time singular control systems are considered. It is generally assumed that the system coefficients depend on time and the controls and observations are unconstrained. Using algebraic methods and the theory of singular differential equations, necessary and sufficient conditions for impulsive controllability and impulsive observability are formulated and proved. In the proofs of the main results canonical decomposition of singular control systems is extensively used. It should be pointed out that these conditions require verification of the images and kernels of linear operators. Moreover, a simple numerical example is given which illustrates the theoretical considerations. Finally, it should be mentioned that the paper contains also several remarks and comments on controllability and observability problems for singular control systems. Moreover, similar considerations can be found in the paper [J. D. Cobb, “Controllability, observability and duality in singular systems”, IEEE Trans. Autom. Control AC-29, 1076–1082 (1984)].

### MSC:

 93B05 Controllability 93B07 Observability 93C05 Linear systems in control theory
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### References:

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