A new approach for estimating controllable and recoverable regions for systems with state and control constraints

In this paper the problem of estimating controllable and recoverable regions for classes of nonlinear systems in the presence of uncertainties, state and control constraints is considered. A new computational technique is proposed based upon a ray-gridding idea in contrast to the usual gridding techniques. The new technique is also based on the positive invariance principle and the use of piecewise linear (PL) Lyapunov functions to generate polytopic approximations to the controllable/recoverable region with arbitrary accuracy. Various types of stabilizing controllers achieving certain trade-offs between robustness, performance and safety, while respecting state and control constraints, can be easily generated. The technique allows the approximation of nonlinear systems via piecewise linear uncertain models which reduces the conservatism associated with linear uncertain models. Copyright © 2002 John Wiley & Sons, Ltd.

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