Control of systems with actuator nonlinearities: an LMI approach

We develop a static, full-state feedback and a dynamic, output feedback control design framework for continuous-time, multivariable, linear, time-invariant systems subject to time-invariant, sector-bounded, input nonlinearities. The proposed framework directly accounts for robust stability and robust performance over the class of input nonlinearities. Specifically, the problem of feedback control design in the presence of time-invariant, sector-bounded, input nonlinearities is embedded within a Lure-Postnikov Lyapunov function framework. Next, a set of linear matrix inequalities are constructed whose solution guarantees closed-loop asymptotic stability, with guaranteed domains of attraction, in the face of time-invariant, sector-bounded, actuator nonlinearities. An illustrative numerical example is presented to demonstrate the effectiveness of the proposed approach.