Saturated stabilization for an uncertain cascaded system subject to an oscillator

This paper investigates saturated stabilization of an uncertain cascaded system that consists of an uncertain double integrator and an uncertain oscillator. The saturation reduction analysis is carried out by using the time-interval based contradiction approach, while the exponential stability analysis of the corresponding reduced system is conducted by using the Hurwitz lemma. In doing the saturation reduction analysis, an intractable problem is how to estimate the states of the oscillator. Fully using the property of saturation functions as well as the technique of Lyapunov inequalities, we can first estimate the states of the oscillator and then achieve the time-derivative bounds that some saturated terms possess in a finite time. This has helped to carry out the saturation reduction analysis. As the applications of the suggested algorithm, the stabilizing controllers have been provided for two benchmark systems — the uncertain two-mass–spring and the translational oscillator with a rotational actuator (TORA).