Stabilizing Controllers for Uncertain Linear Saturating Systems With Additive Disturbances

In this technical brief, the stabilization of an uncertain system with a saturating actuator and an additive disturbance is discussed. The uncertainties and the additive disturbances may be linear, nonlinear, and/or time-varying, but only the upper bounds are assumed known. A linear state feedback control law stabilizes the uncertain system with additive disturbance, and guarantees that, ultimately, the system response lies in a neighborhood of the origin. But the neighborhood cannot be arbitrarily made small by the linear state feedback controller. The proposed approach does not need the solution of a Lyapunov equation or a Riccati equation, therefore the computational burden can be decreased. An example illustrates the application of the proposed method.