Improved Stability Criteria for Linear Neutral Time‐Delay Systems

Abstract

This paper is concerned with the problem of stability analysis of linear neutral time delay systems. First, a new simple Lyapunov-Krasovskii functional is constructed based on delay partitioning approach, then, a novel improved delay-dependent stability criterion is established to guarantee the asymptotic stability of the neutral system. The obtained stability criterion is expressed in terms of linear matrix inequalities, which can be verified easily by means of standard software. Numerical examples are given to illustrate the effectiveness of the proposed method and the advantage over some existing results. 2 2 2 γ .By using the Leibniz-Newton formula, and denoting

Control for Time‐Varying Delay Systems by Integrating Semi‐Discretization and Hysteresis‐Based Switching

“…Later, the introduction of Riccati equations and linear matrix inequality (LMI) greatly promoted the development of those methods and led to a large number of excellent works, e.g. , .…”

“…Prior to 1990's, due to a lack of a general approach to constructing Lyapunov-Krasovskii functionals or Lyapunov functions, only existence conditions could be obtained rather than general solutions. Later, the introduction of Riccati equations [11] and linear matrix inequality (LMI) greatly promoted the development of those methods and led to a large number of excellent works, e.g., [12][13][14].…”

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

“…However, the resulting stability conditions can be strictly conservative due to using bounding techniques for estimating the upper bound of the Lyapunov functional derivatives. Therefore, finding less restrictive stability conditions for time‐delay systems using new LKFs and/or estimating tighter upper bounds of the LKF derivatives is a crucial topic, which has become the focus of numerous researches (see, eg, literature()).…”

“…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. In the meanwhile, the effect of those methods may not be significant in expanding the stability region.…”

“…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, 8,9,12,[15][16][17] using multiple-integral terms, 9,10,12,[18][19][20] and using slack variables or zero equations. 8,15 A number of those schemes can result in the excessive number of decision variables that can imply computational difficulties.…”