Output Feedback Control with Input Saturations: LMI Design Approaches

This paper addresses the control of linear systems with input saturations. We seek a controller that guarantees for the closed-loop system: (i) stability for a given poly tope of initial conditions, (ii) a prescribed weak L2 gain attenuation between inputs and outputs of interest. Two approaches are proposed based on: (i) ensuring that the controller never saturates: the obtained controller is linear time invariant (LTI), (ii) ensuring absolute stability against the saturations: the controller is then linear time varying (LTV). Existence conditions for these two control structures can be cast as (convex) optimization problems over linear matrix inequalities (LMIs). Finally, using numerical experiments, we compare both approaches. In this numerical examples, the LTI controller presents some advantages.

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