Stability Criteria for Periodic Selector-Linear Difference Inclusions

Abstract

The paper considers periodic selector-linear difference inclusions.  Lyapunov functions from a parametric class of homogeneous forms of even degree are constructed. These functions establish necessary and sufficient conditions of asymptotic stability and can be used in the development of numerical  methods for investigating the stability of the systems equivalent to the considered difference inclusions. Using piecewise linear Lyapunov functions, an algebraic criterion of asymptotic stability of the considered inclusions is obtained. An example of a mechanical system leading to periodic selector-linear difference inclusion is considered.