On improved delay-dependent robust stability criteria for uncertain systems with interval time-varying delay

Abstract

This paper considers the problem of delay-dependent robust stability for uncertain systems with interval time-varying delays. By using the direct Lyapunov method, a new Lyapunov-Krasovskii (L-K) functional is introduced based on decomposition approach, when dealing with the time derivative of L-K functional, a new tight integral inequality is adopted for bounding the cross terms. Then, a new less conservative delay-dependent stability criterion is formulated in terms of linear matrix inequalities (LMIs), which can be easily solved by optimization algorithms. Numerical examples are given to show the effectiveness and the benefits of the proposed method.

Nonfragile stabilization for uncertain system with interval time‐varying delays via a new double integral inequality

“…Thus, finding a novel integral inequality for quadratic functions plays a significant part in the proposed study. The main difference and novelty of this proposed approach compared with the existing works, based on AFBII and with the aid of some mathematical approaches, is that a NDII is developed, which plays an alternative tools in the computational analysis process for JDII, WBDII, and some other double integral inequalities.…”

“…Consequently, the need to deeply study the stability of time‐delay systems (TDSs) is of most importance. Therefore, the stability of TDSs was an energetic research field in the last few years and received considerable attention from the scholar society. Nowadays, several efforts have been paid to the issue of TDSs, and a bunch of related literature have been made in this proposed field based on Lyapunov stability theory by way of linear matrix inequality (LMI) technique .…”

“…(iii) The NDII is first time utilized to derive the stability conditions, which plays a significant part in the less conservatism results. (iv) The main outcomes of this report are guaranteed less conservative compared with that in recently existing works . In addition, the calculated MAUBs based on diverse methods are compared in numerical illustrative part.…”

New delay range–dependent stability criteria for interval time‐varying delay systems via Wirtinger‐based inequalities

“…A number of recent endeavours for improving the stability criteria of interval time‐varying delay systems have been devoted to modifying the LKF, and other attempts have focused on reducing the conservatism of the used techniques for estimating the LKF's derivative. The methods of the first group include delay partitioning and delay decomposition schemes,() using multiple‐integral terms,() and using slack variables or zero equations. () A number of those schemes can result in the excessive number of decision variables that can imply computational difficulties.…”

Improved delay‐range‐dependent stability analysis for uncertain retarded systems based on affine Wirtinger‐inequality

“…In past decades, vast literature on improvements of bounding inequalities as well as appropriate choice of L-K functional to fit the usage of bounding inequalities have been reported with an objective to enhance the result of delay upper bound. A detailed chronological review on improvement of the delay upper bound results by developing new methods can be found in [3] and more recent developments can be found in [4,[7][8][9][10][11][12][13][14][15][16][17][18][19][20] and references there in validating the fact that this field of research is still treated as an open problem in computation and control field (see e.g. [3,5] and references therein).…”