This paper deals with a delayed ratio-dependent functional response predator-prey model with a threshold harvesting policy. We study the equilibria of the system before and after the threshold. We show that the threshold harvesting can improve the undesirable behavior such as nonexistence of interior equilibria. The global analysis of the model as well as boundedness and permanence properties a...

This paper is concerned with the problem of stability and stabilization of neutral time-delay systems. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov functional and using some integral inequalities without introducing any free-weighting matrices. On the basis of the obtained stability condition, a stabilizing method is al...

This paper addresses the synthesis of delay-dependent local stabilizing controllers for, possibly open-loop unstable, nonlinear quadratic systems with a varying time-delay in the state. We develop methods for designing static nonlinear quadratic state feedback controllers that guarantee the local asymptotic stability of the closed-loop system zero equilibrium point in some polytopic region of t...

A delay-dependent solution is given for state-feedback H1 control of linear discrete-time systems with unknown constant or time-varying delays and with polytopic or norm-bounded uncertainties. Sufficient conditions are obtained for stability and for achieving design specifications which are based on Lyapunov– Krasovskii functionals via a descriptor representation of the system. Similarly to the...

This paper considers interval time-varying delay systems. The time-delay interval is divided into several zones and the systems switch among the different zones. Based on LyapunovKrasovskii functional methods and linear matrix inequality (LMI) techniques, Exponential stability is exploited for every time-delay zone. The global stability of the switched system is guaranteed if some minimum avera...

This paper deals with the problem of stability and robust control for both certain and uncertain continuous-time singular systems with state delay. Systems with norm-bounded parameter uncertainties are considered. Robust delay-dependent stability criteria and linear memoryless state feedback controllers based on linear matrix inequality are obtained. By choosing some Lyapunov-Krasovskii functio...

This paper deals with the stability problem for a class of linear neutral delaydifferential systems. The time delay is assumed constant and known. Delaydependent criteria are derived. The criteria are given in the form of linear matrix inequalities which are easy to use when checking the stability of the systems considered. Numerical examples indicate significant improvements over some existing...

The problems of delay-dependent robust stability and stabilization of a class of uncertain, linear discrete-time singular systems with state-delay are examined. The parametric uncertainties are assumed to be time-invariant and normbounded appearing in the state and delay matrices. A new system representation is developed to derive new delay-dependent stability criteria without relying on overbo...

Stability of time delay systems is investigated considering the delay-dependent case. The system without delays is assumed stable and conservative conditions are derived for finding the maximal delay that preserves stability. The problem is treated in the quadratic separation framework and the resulting criteria are formulated as feasibility problems of Linear Matrix Inequalities. The construct...

In this note, we provided an improved way of constructing a LyapunovKrasovskii functional for a linear time delay system. This technique is based on the reformulation of the original system and a discretization scheme of the delay. A hierarchy of Linear Matrix Inequality based results with increasing number of variables is given and is proved to have convergence properties in terms of conservat...