Robust stability of state space models with structured uncertainties

In this paper, a method for robust eigenvalue location analysis of linear state-space models affected by structured real parametric perturbations is proposed. The approach, based on algebraic matrix properties, deals with state-space models where system matrix entries are perturbed by polynomial functions of a set of physical uncertain parameters. A method converting the robust stability problem in the nonsingularity analysis of a suitable matrix is proposed. The method leads to positivity check of a multinomial form over a hyperrectangular domain in parameter space. This problem, which can be reduced to finding the real solutions of a system of polynomial equations, simplifies considerably when considering cases with one or two uncertain parameters. For these cases, necessary and sufficient conditions for stability are given in terms of the solution of suitable real eigenvalue problems. © 1990 IEEE