デルタ演算子多項式ポリトープの安定判別法

概要

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Stability analysis of a linear uncertain polynomial system in parameter space is one of central themes of recent control theory. It often requires an enormous number of stability checks with conventional stability test methods. A delta-operator polytopic polynomial, a convex combination of some delta-operator vertex polynomials, is one of such cases. In this paper, robust stability is addressed for polytopic delta-operator polynomials and several necessary and sufficient stability conditions are derived. The delta-operator, an operator used to express discrete-time systems, is known to have significant features; numerical advantage in implementation and ability to smoothly connect z-operator with Laplace operator. Based on this last feature and on the celebrated Edge theorem, we first derive three kinds of exact stability conditions for the uncertain delta-operator polynomials. We then extend the directional stability radius method, which was developed for diamond polynomials, so that it can be also applied to polytopic polynomials. This extension gives rise to the fourth stability test. Furthermore, it is shown from the result of the numerical experiments with these stability analysis methods that one of these four methods, which uses eigenvalues of matrices, turns out to be most efficient for stability analysis of the polytope.
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