Upper Bound Of Delay Derivative Research Articles

Improved delay-derivative-dependent stability criteria for linear systems using new bounding techniques

In this letter, the problem of delay-derivative-dependent stability analysis for linear systems with interval delay is investigated. By constructing variable delay-decomposition Lyapunov-Krasovskii (LK) functional, some delay-derivative-dependent stability criteria are derived by incorporating with different bounding techniques to estimate some integral terms in the derivative of the LK functional. These criteria are efficient when the upper bound of delay derivative is larger than one. These criteria improve the existing ones with smaller computation burden and less conservatism, which are shown through numerical examples.

Observer-based Control for Time–varying Delay Systems with Delay-dependence

This paper is concerned with the problem of observer control of a class of time-varying delay systems with delayed measurements. By using information on delay derivative, improved asymptotic stability conditions for time-delay systems are presented. Unlike previous methods, upper bound of delay derivative is taken into consideration, even if this upper bound is larger than or equal to 1. We develop delay-dependent method for designing linear observer controllers, thus ensuring global uniform asymptotic stabilization for any time delay no larger than a given bound. Numerical examples are given to illustrate effectiveness and less conservatism of obtained stability conditions.

Delay-dependent reliable H ∞ filtering for sector-bounded nonlinear continuous-time systems with time-varying state delays and sensor failures

In this article, the reliable H ∞ filtering problem against sensor failures is investigated for a class of continuous-time systems with simultaneous sector-bounded nonlinearities and varying time delays. The focus of this article is on designing a reliable filter such that the filtering error system is asymptotically stable and meets the prescribed H ∞ norm constraint in the normal case as well as in the sensor failure case simultaneously. Linear matrix inequality conditions, which depend not only on the upper and lower bounds of delay but also on the upper bound of delay derivative, are obtained for the existence of admissible filters and, based on these, the filter design is cast into a convex optimisation problem. What is worth mentioning is that the information about the upper bound of the delay derivative is taken into consideration even if this upper bound is not smaller than 1. A numerical example is presented to illustrate the effectiveness and advantage of the developed filter design method.

Stability and robust stability for systems with a time-varying delay

To concern the stability and robust stability criteria for systems with time-varying delays, this note uses not only the time-varying-delayed state x ( t - h ( t ) ) but also the delay-upper-bounded state x ( t - h ¯ ) to exploit all possible information for the relationship among a current state x ( t ) , an exactly delayed state x ( t - h ( t ) ) , a marginally delayed state x ( t - h ¯ ) , and the derivative of the state x ˙ ( t ) , when constructing Lyapunov–Krasovskii functionals and some appropriate integral inequalities, originally suggested by Park (1999. A delay-dependent stability criterion for systems with uncertain time-invariant delays. IEEE Transactions on Automatic Control, 44(4), 876–877). Two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed. Examples show the resulting criteria outperform all existing ones in the literature.