Worst-case design in the time domain: The maximum principle and the standardH ∞ problem

This paper presents a time-domain, optimal-control approach to worst-case design, an alternative to frequency-domainH _∞ techniques. The generic linear-quadratic set-up of the “standardH _∞ problem” is discussed. The resultsinclude a characterization of suboptimal values, as well as a parametrization of all suboptimal compensators, interms of two coupled indefinite Riccati equations. Both the usual infinite-horizon, time-invariant case and the finite-horizon, time-varying case, are treated. The latter is beyond the scope of frequency-domain analysis. An earlier version of this work was prepared at the Center for Control Sciences, Brown University, and was supported in part by the Air Force Office of Scientific Research under Contract F49620-86-C-011.