New gain-scheduled static output feedback controller design strategy for stability and transient performance of LPV systems

In this study, a new static output feedback (SOF) control for application to linear parameter-varying (LPV) systems is proposed. The asymptotic stability of LPV systems is ensured based on the proposal of a design strategy for gain-scheduled static output feedback (GS-SOF) controllers. The approach selected for the design of the GS-SOF gains is based on a two-stage method, which consists of obtaining a state feedback gain in the first stage, and then in the second stage, using that information to derive the desired GS-SOF controller. In the controller design, the proposed strategy considers performance improvement regarding the specification of the minimum decay rate. The solution for the investigated problem is presented in terms of linear matrix inequalities (LMI) obtained using Finsler's Lemma. Less conservative LMI conditions are also proposed by considering parameter-dependent slack variables. For illustration purposes, the proposed method is implemented in practice for the design of GS-SOF controllers for an active suspension system. In the experiments, it is assumed that only one of its four system state variables is available for the measurement. The dynamic performance achieved in the practical implementation of the designed controllers demonstrates the efficiency of the method.