Robust Stability of Polynomials with Multilinear Parameter Dependence

Abstract The problem is studied of testing for stability a class of real polynomials in which the coefficients depend on a number of variable parameters in a multilinear way. We show that the testing for real unstable roots can be achieved by examining the stability of a finite number of corner polynomials (obtained by setting parameters at their extreme values), while checking for unstable complex roots normally involves examining the real solutions of up to m + 1 simultaneous polynomial equations, where m is the number of parameters. When m = 2, this is an especially simple task.

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