Viability Criteria for a Switched System on Bounded Polyhedron

Abstract

AbstractThe viability of a switched system on a bounded polyhedron set, which is expressed by some linear inequalities, is investigated. Based on nonsmooth analysis and the properties of the tangent cone, a necessary and sufficient condition for viability is proposed. It is shown that the viability of a system is equivalent to the consistency of some systems of linear inequalities. Specifically, a viability condition for a switched system on a bounded polyhedron is presented. According to this condition, determining the viability of a bounded polyhedron can be transformed into verifying certain conditions at vertices of each facet. The method of determining viability, which transforms verifying the condition from infinite points to finite ones, can be implemented easily in practice. An algorithm to determine the viability for the switched system is constructed by using convex analysis. In addition, the approach can be extended to the switched system in which a control input is present. Finally, an example is listed to illustrate the effectiveness of the results.