Practical stabilization of exponentially unstable linear systems subject to actuator saturation nonlinearity and disturbance (Q2731549)

The paper investigates the problem of controlling an exponentially unstable linear system with saturating actuators. This control problem involves issues ranging from such basic ones as controllability and stabilizability to close-loop performances beyond stabilization. In regard to controllability, the issue is the characterization of the null controllable region, the set of all initial states that can be driven to the origin by the bounded input provided by the saturating actuators in a finite time. On the other hand, the issue of stabilizability is the determination of the existence of feedback laws that stabilize the system within the asymptotically null controllable region and the actual construction of these feedback laws. It is well known that if a linear system has its open-loop poles in the closed left-half plane and is stabilizable in the usual linear system sense, then, when subject to actuator saturation, its asymptotically null controllable region is the entire state space. For this reason, such a linear system is usually referred to as asymptotically null controllable with bounded controls.NEWLINENEWLINENEWLINEThe goal of the paper is to design feedback laws that not only achieve semi-global stabilization on the asymptotically null controllable region, but also have the ability to reject bounded disturbance to an arbitrary level of accuracy. The attention of the authors is restricted to systems that have 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. In proving the main results, the continuity and monotonicity of the domain of attraction for a class of second-order systems are revealed.