Robust Stability Domains of Linear Systems with Polynomial Dependency in Uncertain Parameters

Robust Stability Domains of Linear Systems with Polynomial Dependency in Uncertain Parameters

In this paper, a new method is presented for computing the allowable ranges of parameter perturbations in a linear system to maintain stability. For the cases where the coefficients of the characteristic equation are polynomial functions of a single uncertain parameter, a straight-forward method, which only needs to solve several polynomials, is presented. Then, this method is utilized to compute the stability domains in the plane of two uncertain parameters. The properties of the resultant matrix of the characteristic polynomial are used to simplify the procedures.