Minimal-time minimal-order deadbeat regulator with internal stability

This paper is concerned with the output deadbeat (finite settling time) regulation with internal stability for linear discrete-time multivariable systems. The two cases are treated separately; the one is the regulation by state feedback and the other is the regulation through function observers. For both cases, the basic solvability conditions, the minimal settling time and the characterizations of the minimal-time regulators are derived. Throughout the paper, the well-posedness condition plays a fundamental role. A deterministic version of the so-called separation theorem in LQG problem is derived, namely, the minimal-time state-feedback regulator combined with the minimal-time minimal-order function observer yields the overall minimal-time minimal-order regulator by output feedback.