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An iterative approach for the description of null controllable regions of discrete-time linear systems with saturating inputs

An iterative approach for the description of null controllable regions of discrete-time linear systems with saturating inputs,10.1109/MED.2011.5983008

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An iterative approach for the description of null controllable regions of discrete-time linear systems with saturating inputs  
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In this paper an iterative characterization of the null controllable region for discrete-time linear systems subject to input saturation with unstable eigenvalues is proposed. First an outer estimate of the null controllable region by means of invariant hyperparallelograms is obtained and then an iterated convexification technique is developed. Theoretical developments are supported by some illustrative examples. I. INTRODUCTION Input saturation is an operating condition that is well known to the control community for its "side effects" which cause both conventional and adaptive controllers to lose their control performance (i.e., agility/bandwidth and command tracking) as well as stabilization capability. The presence of actuator saturation in control systems, though frequently ignored, is due to inherent (and unavoidable) physical limitations of devices. Existing results pertaining to the problem of global and semi-global stabilization showed that, in general, global stabilization of a linear system subject to saturating actuators can be achieved by a nonlinear controller if and only if the linear system (without saturation) is asymptotically null controllable with bounded control, this condition being equivalent to classical stabilizability and to the requirement that the plant has non exponentially unstable open loop poles (6), (21), (22), (23), (13), (25).
Conference: Mediterranean Conference on Control and Automation - MED , 2011
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