Abstract
A linear discrete-time system represented by delta-operator is known to have an advantage of accuracy in numerical calculations over usual shift-operator systems. Analysis of such a system is a topic of recent times. In this paper, we are interested in stability analysis for delta-operator systems with parametric uncertainties represented by interval polynomials. Though the extreme point results hold for the stability of such polynomials, computational cost becomes markedly enormous when the degree of the polynomials increases. We propose a new stability analysis method for the systems using stability margin in order to reduce the amount of work for stability analysis. We check if a hyperbox of an interval polynomial is contained in the stability region in the coefficient space. To do this, we propose ‘directional stability radius’ as a stability margin estimater. It is a stability radius where coeffient perturbations are supposed to be in certain constrained directions. The devised stability analysis method is to test which vertexes of the hyperbox are covered by certain stability hyperballs with the directional stability radius. By numerical examples, we show that the proposed method is more efficient than brute-force check of every vertex polynomial.
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