Reachable Set Bounding for a Class of Nonlinear Time-Varying Systems with Delay

Xingao Zhu,Yuangong Sun,Fanwei Meng

doi:10.1155/2018/7308476

Xingao Zhu, Yuangong Sun + Show 1 more

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https://doi.org/10.1155/2018/7308476

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Abstract

We investigate the problem of reachable set bounding for a class of continuous-time and discrete-time nonlinear time-varying systems with time-varying delay. Unlike some preceding works, the involved disturbance input and time-varying delay are not assumed to be bounded. By employing an approach which does not involve the conventional Lyapunov-Krasovskii functional, new conditions are proposed such that all the state trajectories of the system converge asymptotically within a ball. Two illustrative examples are also given to show the effectiveness of the obtained results.

Highlights

We investigate the problem of reachable set bounding for a class of continuous-time and discrete-time nonlinear time-varying systems with time-varying delay
Reachable set bounding plays an important role in ensuring safe operation in practical engineering through synthesizing controllers to avoid undesirable regions in the state space [1]
The problem of reachable set bounding with different dynamics has been investigated by many researchers in recent years in [2,3,4,5,6,7], to name a few

Summary

Introduction

Reachable set bounding plays an important role in ensuring safe operation in practical engineering through synthesizing controllers to avoid undesirable (or unsafe) regions in the state space [1]. For a switched system with nonlinear disturbance which can be bounded by a linear system, global exponential stability criteria were established in [29] Inspired by this and motivated by the work in [30, 31], the paper will introduce a new approach which is different from the Lyapunov-Krasovskii functional method to derive new explicit conditions such that all the state trajectories of a class of continuous-time and discrete-time nonlinear time-varying systems with delay converge asymptotically within a ball. The main contribution of this paper is threefold: (1) the nonlinear term considered in this paper takes the more general form, which contains the systems studied in [26,27,28,29] as special cases; (2) the involved disturbance input and time-varying delay are not assumed to be bounded; (3) unlike some existing works, we do not need to transform the system to a timeinvariant one, which leads to less conservative conditions for reachable set bounding.

Preliminaries

Main Results

Numerical Examples

Conclusion