Practical stabilization for piecewise-affine systems: A BMI approach

We propose in this paper, a systematic switching practical stabilization method for PWA switched systems around an average equilibrium. For these systems, the main difficulty comes from the fact that to end in BMI formulation, it is necessary to represent the system in an augmented state space but a restricted one. However, the derived stabilizing conditions are not tractable as BMI in the restricted domain. We will present a method that overcomes this difficulty and drives asymptotically system states into a ball centered on the desired non-equilibrium reference. The efficiency of this practical stabilization method is showed by the ball smallness and the good robustness against disturbances. The design control searches for a single Lyapunov-like function and an appropriate continuous state space partition to satisfy stabilizing properties. Therefore, the method constitutes a simple systematic state feedback computation; it may be useful for on-line applications. As a direct application, satisfactory simulation results are obtained for two illustrative examples, a Buck–Boost converter and a multilevel one. Due to their functioning nature, these devices constitute good examples of switched systems. They are electrical circuits controlled by switches to produce regulated outputs despite the load disturbances and power supply irregularities.