MIMO H∞-control with time domain constraints

The problem of H_∞ optimization subject to time-domain constraints over a finite horizon is considered. Given γ>0 and a set of fixed inputs {wⁱ}, it is required to find a controller such that a closed-loop transfer matrix has an H_∞ norm less than γ, and the time responses to the signals wⁱ belong to some prespecified sets. First, the one-block constrained H_∞ optimal control problem is reduced to a finite-dimensional convex minimization problem and a standard H _∞ optimization problem. Then, the general four-block H_∞ optimal control problem is solved by reduction to the one-block case. The objective function is constructed via state-space methods, and some properties of H_∞ optimal constrained controllers are given. It is shown how satisfaction of the constraints over a finite horizon can imply good behavior overall. An efficient computational procedure based on the ellipsoid algorithm is also discussed