The fuzzy H∞ filter design problem for T-S fuzzy systems with interval time-varying delay is investigated. The delay is considered as the time-varying delay being either differentiable uniformly bounded with delay derivative in bounded interval or fast varying with no restrictions on the delay derivative . A novel Lyapunov-Krasovskii functional is employed and a tighter upper bound of its deriv...

Discontinuous Lyapunov functionals appeared to be very efficient for sampled-data systems (Fridman, 2010; Naghshtabrizi, Hespanha, & Teel, 2008). In the present paper, new discontinuous Lyapunov functionals are introduced for sampled-data control in the presence of a constant input delay. The construction of these functionals is based on the vector extension of Wirtinger’s inequality. These fun...

The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated. By constructing a novel switched Lyapunov–Krasovskii functional, a delay-dependent criterion for the unforced system to be regular, causal and uniformly asymptotically stable is esta...

In this paper, the problem of stability for networked control systems (NCSs) is investigated. Considering both the time-varying network-induced delay and data packet dropouts, NCSs are transformed into typical linear systems with interval time-varying delay. Based on the obtained model, a new delay-dependent stability criteria in terms of linear matrix inequalities (LMIs) is provided by constru...

This paper deals with the problem of stability analysis for networked control systems via the time-delayed system approach. The network-induced delays are modeled as two additive time-varying delays in the closed-loop system. To check the stability of such particular featured systems, an appropriate Lyapunov-Krasovskii functional is proposed and the Jensen inequality lemma is applied to the int...

We study generalized variable projective synchronization between two unified time delayed systems with constant and modulated time delays. A novel Krasovskii-Lyapunov functional is constructed and a generalized sufficient condition for synchronization is derived analytically using the Lyapunov stability theory and adaptive techniques. The proposed scheme is valid for a system of n-numbers of fi...

In this work, novel stability results for load frequency control (LFC) system considering time-varying delays, nonlinearly perturbed load, and disturbance of parameters are proposed by using proportional-integral strategy. Considering the exogenous disturbance, an improved criterion in form linear matrix inequalities (LMIs) is derived simple Lyapunov–Krasovskii functionals (LKFs). The delay-dep...

This paper deals with robust exponential stability of Markovian jumping stochastic Cohen–Grossberg neural networks (MJSCGNNs) with mode-dependent probabilistic time-varying delays, continuously distributed delays and impulsive perturbations. By construction of novel Lyapunov–Krasovskii functional having the triple integral terms, the double integral terms having the positive definite matrices d...

In this paper, we combine a descriptor approach to stability and control of linear systems with time-varying delays, which is based on the Lyapunov Krasovskii techniques, with a recent result on sliding mode control of such systems. The systems under consideration have norm-bounded uncertainties and uncertain bounded delays. The solution is given in terms of linear matrix inequalities (LMIs) an...

When dealing with nonlinear functional differential or difference equations, it is popular to use the concept of Lyapunov functionals to qualitatively analyze their behavior. However, the use of Lyapunov functionals require ingenuity in the construction of such a function and moreover, the end results heavily depend on the constructed Lyapunov functional. For the purpose of illustration we cons...