Improved robust stability criteria for uncertain linear neutral‐type systems via novel Lyapunov‐Krasovskii functional

Abstract

The stability problem for the uncertain time‐varying delayed neutral‐type system is concerned in this paper. By introducing a novel Lyapunov‐Krasovskii functional (LKF) related to a delay‐product‐type function and two delay‐dependent matrices, some new delay‐dependent robust stability sufficient conditions are derived, which are based on convex linear matrix inequality (LMI) framework. The sufficient conditions in this paper can reduce the conservativeness of some recent previous ones. In the end, some numerical examples, including a linear neutral‐type system, the partial element equivalent circuit and a general linear system, show the effectiveness of the proposed method.

Stability analysis for 2‐D switched Takagi‐Sugeno fuzzy systems with stable and unstable subsystems

“…In the past few decades, the theoretical significance and practical applications of the 2-D system has received extensive attention of scholars. Due to the increase of the dimension, there are profound and substantial differences between 2-D system and 1-D system [1][2][3][4][5][6]. Because of the intrinsic differences between them, and the widespread application background [7,8], the research of stability analysis and controller synthesis for 2-D time-delay systems, both in theory and in engineering practice, has great challenge.…”

An enhanced stability criterion for linear time-delayed systems via new Lyapunov–Krasovskii functionals

“…To analyze the stability problem of system (1) based on the Lyapunov theorem [1][2][3][4][5], the main efforts are concentrated on the following several directions: one is finding an appropriate LKF, for example, LKF with delay partitioning approach [6][7][8][9], LKF with augmented terms [10][11][12], LKF with triple-integral and quadruple-integral terms [13,14], and so on. The other is reducing the upper bounds of the time derivative of LKF as much as possible by developing various inequality techniques, such as Jensen inequality [15], Wirtingerbased inequality [16], auxiliary function based inequality [17], Bessel-Legendre inequality [18], and so on.…”

Abel lemma‐based finite‐sum inequality approach to stabilization for 2‐D time‐varying delay systems

“…It is well known that delay‐dependent conditions are reasonable and less conservative than delay‐independent cases, especially when the size of time‐delay is small. As a consequence, the delay‐dependent stability analysis problem has been widely developed for 1‐D time‐delay systems [2–8]. Furthermore,increasing attention has been paid to the stability and control problems for 2‐D systems with state delays due to the strong applications of the 2‐D systems in engineering fields [9].…”