Fixed‐time stabilization for a class of nonlinear time‐delay systems

Abstract

In this paper, we investigate the problem of fixed-time stabilization (FTS) for a class of second-order nonlinear time-delay systems. Using the fixed-time stability theory and Lyapunov-Krasovskii functional, a design scheme of fixed-time stability for time-delay systems is proposed. This scheme effectively solves the adverse impact of time-delay on the system, and and ensure that the corresponding closed-loop system is stable for a fixed time. The main benefit of the proposed control methods is that the influences of time-delay state and nonlinear uncertainties can be effectively attenuated with the help of feedback method. Finally, the simulation is given to show the effectiveness of the design scheme.

Fixed-time stabilization for lower-triangular nonlinear systems under the p-normal form

“…In addition, key dynamic gain methods were utilized to study the FTS of NLSs in Zhang et al (2023). FTS of a class of second-order nonlinear time-delay systems was described in Wang et al (2023). However, the problem of FTS for more general NLSs in the p -normal form has not yet been explored, which motivates the current research.…”

General stability criteria for time‐delay systems using a new delay‐dependent reciprocally convex inequality

“…Time-delay systems (TDSs) have received significant attention due to their prevalent presence in real-world applications [1][2][3]. The presence of time-delays in a system can lead to turbulence or even instability, making it crucial to explore the stability issues of such systems [4][5][6][7]. Consequently, numerous researchers have been drawn to this subject, and significant advancements have been made [8][9][10][11].…”