Discrete-time H2 and H∞ low-gain theory

For stabilization of linear systems subject to input saturation, there exist four different approaches of low-gain design all of which are independently proposed in the literature, namely direct eigenstructure assignment, H2 and H8 algebraic Riccati equation (ARE) based methods, and parametric Lyapunov equation-based method. It is shown in X. Wang et al. (submitted, 2010) that for continuous-time linear systems, all these methods are rooted in and can be unified under two fundamental control theories, H2 and H8 theory. In this paper, we extend such a result to a discrete-time setting. Both the H2 and H8 ARE-based methods are generalized to consider systems where all input channels are not necessarily subject to saturation, and explicit design methods are developed. Copyright (C) 2011 John Wiley & Sons, Ltd.