Reachable Set Bounding for Homogeneous Nonlinear Systems with Delay and Disturbance

Xingao Zhu,Yuangong Sun

doi:10.1155/2019/8698294

Xingao Zhu, Yuangong Sun

Open Access

https://doi.org/10.1155/2019/8698294

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Journal: Complexity	Publication Date: Jul 1, 2019
Citations: 4	License type: CC BY 4.0

Affiliation: Qufu Normal University, University of Jinan

Abstract

Reachable set bounding for homogeneous nonlinear systems with delay and disturbance is studied. By the usage of a new method for stability analysis of positive systems, an explicit necessary and sufficient condition is first derived to guarantee that all the states of positive homogeneous time-delay systems with degree p>1 converge asymptotically within a specific ball. Furthermore, the main result is extended to a class of nonlinear time variant systems. A numerical example is given to demonstrate the effectiveness of the obtained results.

Highlights

Recent years have witnessed a rapid development of reachable set bounding for linear systems in [1,2,3,4,5,6,7,8,9,10,11], to name a few
Less attention has been paid to reachable set bounding for nonlinear time-delay systems
The same problem was considered in [24] for homogeneous positive systems of degree p > 1, while time delay was not taken into consideration

Summary

Introduction

Recent years have witnessed a rapid development of reachable set bounding for linear systems in [1,2,3,4,5,6,7,8,9,10,11], to name a few. In most of existing references, the traditional LyapunovKrasovskii function method is most commonly used Such a method is usually difficult to derive explicit conditions for reachable set estimation of nonlinear systems with delay and disturbance. Less attention has been paid to reachable set bounding for nonlinear time-delay systems. Reachable set bounding for continuous-time and discrete-time homogeneous time-delay positive systems of degree one was studied in [22]. By developing the methods used in [23, 24], we first establish a necessary and sufficient condition such that all the solutions of positive homogeneous time-delay systems with degree p > 1 converge asymptotically within a specific ball, which contains those results in [23, 24] in special cases. An n × n-dimensional matrix A is called Metzler if all its off-diagonal entries are nonnegative

Preliminaries

Main Results

Numerical Example

Conclusion