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This paper considers the robust stability for a class of linear neutral systems with interval time-varying delay and nonlinear perturbations. A Lyapunov Krasovskii functional, which takes the range information of the time-varying delay into account, is proposed to analyze the stability. A novel approach is established for estimating the upper bound on the time derivative of the Lyapunov Krasovskii functional, and by utilizing free weighting matrices, new delay-range-dependent stability criteria are introduced in terms of linear matrix inequalities. Numerical examples are given to show the effectiveness of the proposed approach.

This paper studies the problem of H∞ output tracking control for neutral delay system with nonlinear perturbations. Based on a novel augmented Lyapunov functional, a sufficient condition for the existence of state-feedback controller is presented in terms of linear matrix inequality, which not only guarantees the stability of closed-loop system, but also ensure the output of the neutral system tracks the output of a given reference model in the H∞ sense.

The robust non-fragile H ∞ control problems for stochastic systems with time-varying delay and nonlinear perturbation are investigated in this paper. Firstly, the delay-dependent stochastic bounded real lemmas are obtained in terms of linear matrix inequality. Then, based on the stochastic bounded real lemma, for the additive controller uncertainties, the non-fragile controllers are designed by solving a LMI. A numerical example is given to show the validity of the obtained results and the effectiveness of the proposed method.

Two extended cooperative driving lattice hydrodynamic models are proposed by considering the backward looking effect in traffic flow. The stability conditions for the two models are investigated with the linear stability theory and it is found that new consideration leads to the improvement of the stability of traffic flow. The modified Korteweg-de Vries equations (the mKdV equation, for short) near the critical point are derived by using the nonlinear perturbation method to show that the traffic jam could be described by the kink-antikink soliton solutions for the mKdV equations. Moreover, the anisotropy of traffic flow is further discussed through examining the negative propagation velocity as the effect of following vehicle is involved.

In this paper the stability of multi-periodic repetitive control problem, where two or more periods exist in the reference and disturbance signals, is studied. A Lyapunov analysis is used to prove L 2 m (0,∞) ∩L ∞ m (0,∞) stability for a class of passive nonlinear systems subject to a class of nonlinear perturbations. A proof of exponential stability under a strictly positive real condition is provided.