Abstract
A method of verifying the viability criterion at a given point for a region with nonsmooth boundary, which is expressed by a quasidifferentiabl 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.
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This research is supported by the National Natural Science Foundation of China under Grant No. 10671126 and Shanghai Leading Academic Discipline Project under Grant No. S30501.
This paper was recommended for publication by Editor Jinhu LÜ.
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Gao, Y. Viability criteria for differential inclusions. J Syst Sci Complex 24, 825–834 (2011). https://doi.org/10.1007/s11424-011-9056-6
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DOI: https://doi.org/10.1007/s11424-011-9056-6