H∞ optimal control with time-domain constraints: numerical aspects and examples

Standard H_∞ optimization cannot handle specifications or constraints on the time response of a closed-loop system exactly. Constrained H_∞ Optimization [10,9] allows the design of control laws which minimize the infinity norm of a (weighted) closed loop transfer function (matrix) under the requirements of closed loop stability and constraints on several closed loop time responses to test signals (steps, impulses, etc.) over a finite horizon. This formulation provides a systematic tool to trade-off frequency and time domain specifications exactly and is ideally suited for control problems with a combination of frequency domain (robustness, noise attenuation) and time domain (settling times, limited control action) specifications. In this paper, we first review the basic ideas behind Constrained H_∞ optimization. Then, we discuss issues pertaining to the numerical application of the method and illustrate the theory by means of simple design examples.