Robust non‐fragile<i>H</i>_∞ ∕ <i>L</i>₂ − <i>L</i>_∞control of uncertain linear system with time‐delay and application to vehicle active suspension

Summary This paper presents an approach to design robust non‐fragile H ∞ ∕ L 2 − L ∞ static output feedback controller, considering actuator time‐delay and the controller gain variations, and it is applied to design vehicle active suspension. According to suspension design requirements, the H ∞ and L 2 − L ∞ norms are used, respectively, to reflect ride comfort and time‐domain hard constraints. By employing a delay‐dependent Lyapunov function, existence conditions of delay‐dependent robust non‐fragile static output feedback H ∞ controller and L 2 − L ∞ controller are derived, respectively, in terms of the feasibility of bilinear matrix inequalities. Then, a new procedure based on LMI optimization and a hybrid algorithm of the particle swarm optimization and differential evolution is used to solve an optimization problem with bilinear matrix inequality constraints. Simulation results show that the designed active suspension system still can guarantee their own performance in spite of the existence of the model uncertainties, the actuator time‐delay and the controller gain variations. Copyright © 2014 John Wiley &amp; Sons, Ltd.