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Analysis and design for discrete-time linear systems subject to actuator saturation. (English) Zbl 0987.93027
Summary: We present a method to estimate the domain of attraction for a discrete-time linear system under a saturated linear feedback. A simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant. Moreover, the condition can be expressed as linear matrix inequalities (LMIs) in terms of all the varying parameters and hence can easily be used for controller synthesis. The following surprising result is revealed for systems with single input: suppose that an ellipsoid is made invariant with a linear feedback, then it is invariant under the saturated linear feedback if and only if there exists a saturated (nonlinear) feedback that makes the ellipsoid invariant. Finally, the set invariance condition is extended to determine invariant sets for systems with persistent disturbances. LMI based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements.
##### MSC:
 93B50 Synthesis problems 93C55 Discrete-time control systems 93D20 Asymptotic stability of control systems 93B51 Design techniques in systems theory 93C10 Nonlinear control systems 93C73 Perturbations in control systems 15A39 Linear inequalities of matrices