How to match an affine time-varying feedback law: Properties of a new parameterization for the control of constrained systems with disturbances

This paper is concerned with the application and analysis of a recent result in the literature on robust optimization to the control of linear discrete-time systems, which are subject to unknown state disturbances and mixed constraints on the state and input. By parameterizing the control input sequence as an affine function of the disturbance sequence, it can be shown that a certain class of robust finite horizon control problems can be solved in a computationally tractable fashion, provided the constraint and the disturbance sets are polytopic. The main contribution of the paper, as the title suggests, is to show that this parameterization includes the class of affine time-varying state feedback control laws. The paper also shows how this parameterization can be used to efficiently synthesize receding horizon and minimum-time control laws that are robustly invariant. Two small numerical examples are also presented that highlight some of the strengths and limitations of the proposed parameterization.