State feedback <i>H</i> _∞ control design using asymmetric Lyapunov–Krasovskii functional for vehicle active suspension system

This paper presents a state feedback H ∞ control design for active suspension systems with time-delays using an asymmetric Lyapunov–Krasovskii functional (LKF). Less conservative stabilization conditions are derived in this paper for the design of a state feedback control synthesis through asymmetric LKF in the linear matrix inequalities (LMIs). This investigation aims to exploit the capability of asymmetric LKF to minimize conservativeness and utilizes Jensen’s and Wirtinger’s bounded integral inequalities to handle cross-terms in the asymmetric LKF derivative. One of the key benefits of the asymmetric LKF, compared to symmetric LKF, is its capability to provide less conservative stability conditions by relaxing the condition that all the matrix variables should be symmetric or positive definite. Capitalizing on the potential of asymmetric LKF to realize a less conservative state feedback H ∞ control design, this study evaluates the performance on a multi-objective quarter-vehicle active suspension system (ASS) for various realistic road profiles. Simulation results of bump road surface and random road profiles along with the frequency responses indicate that despite the time delays in the feedback loop the proposed H ∞ controller improves the closed-loop suspension system performance significantly. Quantitative analysis of the chassis acceleration and suspension travel corroborates that compared to the performance of H ∞ controller and predictor-based feedback controller designed using symmetrical LKF, the proposed control scheme reduces the body acceleration and tyre deflection RMS values by 16.5% and 8% when compared to H ∞ control and by 21.5% and 13.5% when compared to predictor-based state feedback control, respectively.