Absolute stability of time-varying delay Lurie indirect control systems with unbounded coefficients

Fucheng Liao,Xiao Yu,Jiamei Deng

doi:10.1186/s13662-017-1094-5

Abstract

This paper investigates the absolute stability problem of time-varying delay Lurie indirect control systems with variable coefficients. A positive-definite Lyapunov-Krasovskii functional is constructed. Some novel sufficient conditions for absolute stability of Lurie systems with single nonlinearity are obtained by estimating the negative upper bound on its total time derivative. Furthermore, the results are generalised to multiple nonlinearities. The derived criteria are especially suitable for time-varying delay Lurie indirect control systems with unbounded coefficients. The effectiveness of the proposed results is illustrated using simulation examples.

Highlights

In the middle of the last century, the concept of absolute stability was introduced in [ ]
The absolute stability problem of Lurie system has been extensively studied in the academic community, and there have been many publications on this topic [ – ]
In [ ], Khusainov and Shatyrko studied the absolute stability of multi-delay regulation systems

Summary

Introduction

In the middle of the last century, the concept of absolute stability was introduced in [ ]. As for time-delay Lurie systems with constant coefficients, fruitful results have been obtained. In [ ], by applying the properties of M-matrix and selecting an appropriate Lyapunov function, Chen et al established new absolute stability criteria for Lurie indirect control system with multiple variable delays, and they improved and generalised the corresponding results in [ ]. In [ ], the absolute stability of Lurie indirect control systems and large-scale systems with multiple operators and unbounded coefficients were studied. The authors in [ , ] developed some sufficient conditions for the absolute stability of Lurie direct control systems and large-scale systems with unbounded coefficients. We will study the absolute stability of time-varying Lurie indirect control systems with time delay. The above criteria are true for Lurie systems with constant coefficients

Absolute stability of Lurie systems with multiple nonlinearities

Conclusion