In this paper, a basic property that a Liapunov-Krasovskii functional must have when used for studying the stability of time delay systems under Carath¶eodory conditions is studied. This property concerns the equality, almost everywhere, of the upper right-hand Dini derivative of the Liapunov-Krasovskii functional evaluated at the solution, and of the Liapunov-Krasovskii derivative (computed by...

Robustness is established for the predictor feedback for linear time-invariant systems with respect to possibly time-varying perturbations of the input delay, with a constant nominal delay. The prior results have addressed qualitatively constant delay perturbations (robustness of stability in L2 norm of actuator state) and delay perturbations with restricted rate of change (robustness of stabil...

Robust stability and the guaranteed cost control problem are considered for discrete-time systems with time-varying delays from given intervals. A new construction of Lyapunov– Krasovskii functionals (LKFs), which has been recently introduced in the continuous-time case, is applied. To a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the ...

In this article, we are interested in analysing stability of systems that incorporate time-varying delays in their dynamic. The Lyapunov-Krasovskii approach is definitely the most popular method to address this issue and many results have proposed new functionals and enhanced techniques for deriving less conservative stability conditions. In this present work, we propose an original approach: t...

This paper investigates the robust stability problem of Hopfield neural networks(HNNs) with time-varying delay. Two novel LMI-based delay-dependent robust stability criteria are obtained by constructing appropriate Lyapunov-Krasovskii functional. This new criteria based on the free-weighting matrices approach prove to be less conservativeness, which not only retain any useful terms in the deriv...

Sampled-data output-feedback H∞ control of linear systems is considered. The only restriction on the sampling and hold is that the distances between the sequel sampling times and holding times are not greater than given bounds.A new approach, which was recently introduced to sampled-data state-feedback stabilization, is developed to the H∞ control. The system is modelled as a continuous-time on...

This paper addresses the robust consensus control design for input-delayed multi-agent systems subject to parametric uncertainties. To deal with the input delay, the Artstein model reduction method is employed by a state transformation. The input-dependent integral term that remains in the transformed system, due to the model uncertainties, is judiciously analysed. By carefully exploring certai...

For neural networks with constant or time-varying delays, the problems of determining the exponential stability and estimating the exponential convergence rate are studied in this paper. An approach combining the Lyapunov-Krasovskii functionals with the linear matrix inequality is taken to investigate the problems, which provide bounds on the interconnection matrix and the activation functions,...

In this paper, adaptive neural control is proposed for a class of multi-input multi-output (MIMO) nonlinear unknown state time-varying delay systems in block-triangular control structure. Radial basis function (RBF) neural networks (NNs) are utilized to estimate the unknown continuous functions. The unknown time-varying delays are compensated for using integral-type Lyapunov-Krasovskii function...

Funding information PROMETEOII/2013/004; Conselleria d'Educació; Generalitat Valenciana, Grant/Award Number: TIN2014-56158-C4-4-P-AR; Ministerio de Economía y Competitividad, Grant/Award Number: FPI-UPV 2014; Universitat Politècnica de València Summary The problem of output stabilization and disturbance rejection for input-delayed systems is tackled in this work. First, a suitable transformatio...