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Stability and stabilization of mechanical systems with switching. (English. Russian original) Zbl 1229.93099
Autom. Remote Control 72, No. 6, 1143-1154 (2011); translation from Avtom. Telemekh. 2011, No. 6, 5-17 (2011).
Summary: Hybrid mechanical systems with switched force fields, whose motions are described by differential second-order equations are considered. We propose two approaches to solving problems of analysis of stability and stabilization of an equilibrium position of the named systems. The first approach is based on the decomposition of an original system of differential equations into two systems of the same dimension but of first order. The second approach is basing on a direct construction of a general Lyapunov function for a mechanical system with switching.

MSC:
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
70Q05 Control of mechanical systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93B11 System structure simplification
93C15 Control/observation systems governed by ordinary differential equations
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