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Robust stability, minimax stabilization and maximin testing in problems of semi-automatic control. (English) Zbl 1335.93105

Sadovnichiy, Viktor A. (ed.) et al., Continuous and distributed systems II. Theory and applications. Cham: Springer (ISBN 978-3-319-19074-7/hbk; 978-3-319-19075-4/ebook). Studies in Systems, Decision and Control 30, 247-265 (2015).
Summary: The conditions about the problem of robust stability for systems of differential equations with bounded external perturbations are obtained from the solution of the problem of maximum deviation using an extension of the definition of Duboshin and Malkin on stability under permanent perturbations. Further, a linear controlled system with close-loop control is under consideration. Solutions of minimax stabilization problem and a problem of maximin testing in a stability region with given stability factor are described both for finite and infinite stabilization time.
For the entire collection see [Zbl 1342.00018].

MSC:

93D15 Stabilization of systems by feedback
93D09 Robust stability
34D10 Perturbations of ordinary differential equations
49K35 Optimality conditions for minimax problems
49N10 Linear-quadratic optimal control problems
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