SUMMARYThis paper studies the design problem of robust delay-dependent H ∞ controller for a class of timedelay control systems with time-varying state and input delays, which are assumed to be noncoincident. The system is subject to norm-bounded uncertainties and L 2 disturbances. Based on the selection of an augmented form of Lyapunov-Krasovskii (L-K) functional, first a Bounded Real Lemma (BRL) is obtained in terms of linear matrix inequalities (LMIs) such that the nominal, unforced time-delay system is guaranteed to be globally asymptotically stable with minimum allowable disturbance attenuation level. Extending BRL, sufficient delay-dependent criteria are developed for a stabilizing H ∞ controller synthesis involving a matrix inequality for which a nonlinear optimization algorithm with LMIs is proposed to get feasible solution to the problem. Moreover, for the case of existence of norm-bounded uncertainties, both the BRL and H ∞ stabilization criteria are easily extended by employing a well-known bounding technique. A plenty of numerical examples are given to illustrate the application of the proposed methodology of this note. The achieved numerical results on the maximum allowable delay bound and minimum allowable disturbance attenuation level are exhibited to be less conservative in comparison to those of existing methods in the literature.

There always exists a conflict between ride comfort and suspension deflection performances during the vibration control of suspension systems. Active suspension control systems, which are designed by linear methods, can only serve as a trade-off between these conflicting performance criteria. Both performance objectives can only be accomplished at the same time by using a nonlinear controller. This paper addresses the non-linear induced L2 control of an active suspension system, which contains non-linear spring and damper elements. The design method is based on the linear parameter varying (LPV) model of the system. The proposed method utilizes the bilinear damping characteristic, stiffening spring characteristic when the suspension deflection approaches the structural limits, mass variations and parameter-dependent weighting filters. Simulation studies both in time and frequency domain demonstrate that the active suspension system controlled by the proposed method always guarantees an agreement between acceleration (comfort) and suspension deflection magnitudes together with a high ride performance.

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This article addresses the design of a gain-scheduling type nonlinear controller for a full-vehicle active suspension system. The proposed method is based on a Linear Parameter Varying (LPV) model of the system. In this model, the variations in suspension deflection and mass are chosen as the scheduling parameters. During the simulations, the full-vehicle system that is controlled by the proposed method is tested with different road profiles, having high and low bumps, hollows and combinations of the two. The simulation results demonstrate that the proposed method successfully maximizes the ride comfort when suspension deflection is far away from the structural limits and minimizes the suspension deflection by changing its behavior when the suspension limits are reached.