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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.
93B50Synthesis problems
93C55Discrete-time control systems
93D20Asymptotic stability of control systems
93B51Design techniques in systems theory
93C10Nonlinear control systems
93C73Perturbations in control systems
15A39Linear inequalities of matrices