Viability criteria for differential inclusions. (English) Zbl 1269.93046

Summary: A method of verifying the viability criterion at a given point for a region with nonsmooth boundary, which is expressed by a quasi-differentiable function, under a differential inclusion which is a convex hull of finitely many functions, is proposed. By this method, determining the viability is transformed into solving a number of systems of linear inequalities, or equivalently solving a number of linear programming problems. For the other differential inclusion, called the generalized convex process, it is shown that viability condition holds for a polytope if and only if it holds at all of its vertices. This result is an extension of corresponding one for a linear control system.


93C25 Control/observation systems in abstract spaces
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