Abstract
The discrete-continuous systems are considered as the systems with impulsive inputs, which cause the discontinuous behaviour of the system paths. The robustness for nonlinear discrete-continuous systems means the stability of the system path with respect to the approximation of pure impulsive inputs by ordinary ones. Necessary and sufficient conditions of this type of robustness give the opportunity to extract rather narrow class of robust systems. Although robust systems look like very attarctive from theoretical point of view and have many of usefull features, the great part of dynamical system which are of a practical interest are non-robust, and some nontraditional theoretical tools are necessary for their treatment. In this paper the problem of description and path representation in the form of differential equation with a measure is considered. Some specific features of non-robust systems are discussed from the point of controllability. It was shown that non-robust systems can provide the additional controllability opportunities by using the impulsive inputs.
This work was supported in part by National Science Foundation of USA grant CMS 94-1447s and International Association for the Promotion of Cooperation with Scientists from the Independent States of the Former Soviet Union (INTAS) grants 94-697 and 93-2622
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Miller, B.M. (1997). Representation of robust and non-robust solutions of nonlinear discrete-continuous systems. In: Maler, O. (eds) Hybrid and Real-Time Systems. HART 1997. Lecture Notes in Computer Science, vol 1201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014728
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DOI: https://doi.org/10.1007/BFb0014728
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