Robust stability for time-delay systems: the edge theorem and graphical tests
作者： M. Fu , A.W. Olbrot , M.P. Polis
DOI: 10.1109/9.29423
关键词: Counterexample 、 Birkhoff polytope 、 Vertex enumeration problem 、 Convex polytope 、 Kharitonov's theorem 、 Edge (geometry) 、 Discrete mathematics 、 Polytope 、 Combinatorics 、 Mathematics 、 Ehrhart polynomial
摘要: The robust stability problem is discussed for a class of uncertain delay systems where the characteristic equations involve polytope P quasi-polynomials (i.e. polynomials in one complex variable and exponential powers variable). Given set D plane, goal to find constructive technique verify whether all roots every quasi-polynomial belong (that is, D-stability P). First it demonstrated by counterexample that Kharitonov's theorem does not hold general systems. Next shown under mild assumption on D-stable if only edges are D-stable. This extends edge polynomials. third result gives graphical test checking which especially simple when open left-half plane. An application given demonstrate power results. >
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