Delay-Hybrid-Dependent Stability for Systems With Large Delays

Abstract

This paper investigates a problem of stability analysis for a class of nonlinear systems with a time-varying delay taking both large and small values in an alternating manner. This problem is a delay-dependent stability analysis one but it shares some features with delay-independent ones. Hence traditional stability analysis techniques for systems with delay do not apply. By building upon our previous works, we first introduce the concept of delay-hybriddependent stability, which grasps the features of the delays described above. To ease the problem we investigate, we represent the studied system as a system with a switched delay. Then by using switching techniques and Lyapunov-Krasovskii functionals (LKFs), we provide a new stability criterion. Next, in the linear context, we show how the needed LKFs can be constructed by developing an original design of LKFs.

Distributed Optimization for Aggregative Games Based on Euler-Lagrange Systems With Large Delay Constraints

“…In fact, communication or information exchange among players play a key role in solving aggregative games. Hence, the data transmission by means of wireless communication channels may suffer from the effects of time-varying delay or packet dropouts, which inevitably reduce the control performance and even instability [15], [16]. In view of this, it is of great importance to investigate time delays in aggregative games for distributed optimization.…”

Stability analysis of switched nonlinear delay systems with sampled‐data inputs

“…24 On the other hand, delays frequently exist in kinds of modern biological models and engineering systems, including teleoperation systems, electrical networks, and robot systems. [25][26][27][28][29][30][31] Sun et al 26 established stability conditions for nonlinear large delay systems. Zhao et al 27 utilized multiple Lyapunov-Krasovskii functionals to explore the stability for switched linear positive delay systems.…”