This paper considers the problem of stabilization of discrete-time systems with actuator nonlinearities. The proposed framework is based on a linear matrix inequality (LMI) approach and directly accounts for robust stability and robust performance over the class of actuator nonlinearities. Furthermore, it is directly applicable to actuator saturation control and provides state feedback controllers with guaranteed domains of attraction.
IntroductionIn feedback control systems, actuator nonlinearities, such as saturation, arise frequently in practice and can severely degrade closed-loop system performance and in some cases drive the system to instability. For continuous-time systems, the problem of actuator saturation has been widely studied and an extensive literature is devoted to it (see, e.g., [4,9] and the numerous references therein). For discrete-time systems, Riccati equation-based global and semi-global stabilization techniques for actuator saturation have been developed in [7]. In addition, the ap lication of an anti-windup actuator saturation control {amework to discrete-time systems is given in [SI. Finally, in a recent paper [5], a Riccati equation-based global and local static, output feedback control design framework for discrete-time systems with general time-varying, sector-bounded, input nonlinearities was developed.In this aper, we develop an LMI formulation for fullstate feedtack control of systems with input nonlinearities. As demonstrated in this paper, static, full-state feedback control of discrete-time systems with timevarying, sector-bounded, actuator nonlinearities leads to a matrix inequality that is nonlinear in the decision variables; hence, circumventin a direct application of the LMI theory. By over-boun8ing several terms in the nonlinear matrix inequality (NMI), in this paper, we provide tractable sufficient conditions, in the form of LMIs, for feedback control of systems with time-varying, sectorbounded, actuator nonlinearities. Nomenclature
