Yurii V. Nepomnyashchikh

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Continuing the authors’ studies of hybrid dynamical systems, i.e. differential equations governed by finite automata, an efficient and complete classification of control linear systems in the plane is offered. The set of all such systems is divided into equivalence classes which are explicitly characterized by some quantitative invariants. The canonical(More)
We study so-called "hybrid feedback stabilizers" for an arbitrarily general system of linear di erential equations. We prove that under assumptions of controllability and observability there exists a hybrid feedback output control which makes the system asymptotically stable. The control is designed by making use of a discrete automaton implanted into the(More)
We suggest some criteria for the stabilization of planar linear systems via linear hybrid feedback controls. The results are formulated in terms of the input matrices. For instance, this enables us to work out an algorithm which is directly suitable for a computer realization. At the same time, this algorithm helps to check easily if a given linear 2× 2(More)
with a control u = u(y). Here u again depends only on the output y = ξ. It can be shown (see e.g. [1]) that there is no output feedback control of the form u = f(ξ) = f(ξ(t)) that makes the system (2) asymptotically stable. Therefore, it was suggested in [1] to use hybrid feedback controls (abbr. HFC), which indeed can stabilize the system (2). The idea(More)
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