A state‐dependent switching controller design approach for linear systems under control constraints

Abstract

In the present work, a state-dependent switching controller design approach for controlled systems under control constraints is proposed. First, the controlled system with control gain parameters is converted into a single-degree-of-freedom vibration system by using an invertible transform. Second, based on the physical significance of the single-degreeof-freedom linear vibration systems, two pairs of gain parameters are properly chosen to obtain two subsystems with sufficiently small equivalent negative-damping coefficients and sufficiently large equivalent stiffness coefficient difference. Third, by introducing an identical invertible transform, two subsystems are converted into the form of vibration systems simultaneously. As such, it is reasonable to compare the two corresponding energy functions directly. Fourth, two switching lines with maximum and minimum energy ratio between two subsystems are derived to construct a state-dependent switching law. Combining the selected control gain parameters, a state-dependent switching controller is then designed for stabilizing the original controlled system with control constraints. In the end, the effectiveness and robustness of the developed control approach are illustrated by three numerical examples.