CLOSED FORMULAE FOR THE GENERALIZED ℋ∞ SENSITIVITY MINIMIZATION PROBLEM

Abstract

The paper presents a complete solution for the multivariable, continuous-time Generalized ℋ︁∞ (𝒢ℋ︁∞) sensitivity minimization problem. In contrast with existing solutions, derived via polynomial methods, the state-space solution given here is essentially non-iterative. Closed formulae for the minimum and a particular optimal controller are derived in terms of a real Schur decomposition, the solution of two Lyapunov equations and a single, well-conditioned eigenvalue problem. © 1997 by John Wiley & Sons, Ltd.