Local stabilization of discrete-time linear systems with saturating controls: an LMI-based approach

This note has developed a sliding-mode controller which requires only output information for a class of uncertain linear systems. The controller comprises both linear and nonlinear components and is static in nature, i.e., no compensation/observation is included. The novelty of the approach is in the rationale and method used to synthesize the linear control component. The reachability condition is not required to be satisfied globally. Instead, sliding is only expected to take place within a subset of the state-space containing the origin referred to as the sliding patch. This region is shown to be rendered invariant by the control law. The linear static output feedback control component is synthesized using an LMI optimization. The resulting LMI formulation can be solved easily by standard commercially available software. The efficacy of the approach has been demonstrated on a numerical example taken from the sliding-modeliterature. Output feedback sliding-modedesign for linear uncertain systems, " Proc. Inst. Spurgeon, " sliding-mode stabilization of uncertain systems using only output information, " Int. , " Output feedback variable structure control design using dynamic compensation for linear systems, " in Proc. Numerical methods to design the reaching phase of output feedback variable structure control, " Robust output feedback stabilization of uncertain dynamic systems with bounded controllers, " Int. On sliding observers for nonlinear systems, " ASME: J. A nonlinear control strategy for robust sliding-mode performance in the presence of unmatched uncertainty, " Int. Abstract—This note deals with the problem of local stabilization of linear discrete-time systems subject to control saturation. A linear matrix inequal-itie-based framework is proposed in order to compute a saturating state feedback that stabilizes the system with respect to a given set of admissible initial states and, in addition, guarantees some dynamical performances when the system operates in the zone of linear behavior (i.e., when the controls are not saturated).