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 H∞ algebraic Riccati equation (ARE) based methods, and parametric Lyapunov equation based method. We show here all these methods are rooted in and can be unified under two fundamental control theories, H2 and H∞ theory. Moreover, both the H2 and H∞ ARE based methods are generalized to consider systems where all input channels are not subject to saturation, and explicit design methods are developed.