Optimal Solutions to Robust Stabilization Problem for a Class of Systems with Parametric Uncertainty

This paper tackles the robust stabilization problem for the plant family described by the transfer function set P(s, δ, δ) whose coefficients of the denominator and the numerator polynomials are affine in a real uncertain parameter vector δ satisfying the norm constraint ||δ||p ≤ δ for p ≥ 1. It is shown that there exists a fixed controller robustly stabilizing all the members of P(s, δ, δ) if and only if its every member plant is free of unstable pole-zero cancelation. The optimal robust stabilizer is characterized in terms of a three dimensional frequency dependent Hahn-Banach minimizer. Classes of P(s, δ, δ) are characterized using Nevanlinna-Pick interpolation theory. For these classes optimal robust stabilizers can be obtained in closed forms using ℋ∞-optimization technique.