Non-fragile multi-objective static output feedback control of vehicle active suspension with time-delay

This paper presents an approach to design a delay-dependent non-fragile H∞/L2–L∞ static output feedback (SOF) controller for active suspension with input time-delay. The control problem of quarter-car active suspension with actuator time-delay is formulated to a H∞/L2–L∞ control problem. By employing a delay-dependent Lyapunov function, new existence conditions of delay-dependent non-fragile SOF H∞ controller and L2–L∞ controller are derived, respectively, in terms of the feasibility of bilinear matrix inequalities (BMIs). Then, a procedure based on linear matrix inequality optimisation and a hybrid algorithm of the particle swarm optimisation and differential evolution is used to solve an optimisation problem with BMI constraints. Design and simulation results of non-fragile H∞/L2–L∞ controller for active suspension show that the designed controller not only can achieve the optimal performance and stability of the closed-loop system in spite of the existence of the actuator time-delay, but also has significantly improved the non-fragility characteristics over controller perturbations.