Design of fixed-order stabilizing and ℋ 2 - ℋ ∞ optimal controllers: An eigenvalue optimization approach

Abstract

An overview is presented of control design methods for linear time-delay systems, which are grounded in numerical linear algebra techniques such as large-scale eigenvalue computations, solving Lyapunov equations and eigenvalue optimization. The methods are particularly suitable for the design of controllers with a prescribed structure or order. The analysis problems concern the computation of stability determining characteristic roots and the computation of ℋ 2 and ℋ ∞ type cost functions. The corresponding synthesis problems are solved by a direct optimization of stability, robustness and performance measures as a function of the controller parameters. © 2012 Springer-Verlag GmbH Berlin Heidelberg.