Practical stabilization of exponentially unstable linear systems subject to actuator saturation nonlinearity and disturbance

This paper investigates the problem of practical stabilization for linear systems subject to actuator saturation and input additive disturbance. Attention is restricted to systems with two anti-stable modes. For such a system, a family of linear feedback laws is constructed that achieves semi-global practical stabilization on the asymptotically null controllable region. This is in the sense that, for any set chi (0) in the interior of the asymptotically null controllable region, any (arbitrarily small) set chi (infinity) containing the origin in its interior, and any (arbitrarily large) bound on the disturbance, there is a feedback law from the family such that any trajectory of the closed-loop system enters and remains in the set chi (infinity) in a finite time as long as it starts from the set chi (0). In proving the main results, the continuity and monotonicity of the domain of attraction for a class of second-order systems are revealed. Copyright (C) 2001 John Wiley & Sons, Ltd.