Robustness analysis for linear dynamical systems with linearly correlated parametric uncertainties

The authors propose an approach for robust pole location analysis of linear dynamical systems with parametric uncertainties. Linear control systems with characteristic polynomials whose coefficients are affine in a vector of uncertain physical parameters are considered. A design region in complex plane for system pole placement and a nominal parameter vector generating a characteristic polynomial with roots in that region are given. The proposed method allows the computation of maximal domains bounded by linear inequalities and centered at the nominal point in system parameter space, preserving system poles in the given region. The solution of this problem is shown to also solve the problem of testing robot location of a given polytope of polynomials in parameter space. It is proved that for stability problems for continuous-time systems with independent perturbations on polynomial coefficients, this method generates the four extreme Kharitonov polynomials