A novel descriptor redundancy method based on delay partition for exponential stability of time delay systems

Abstract

This paper investigates the exponential stability of uncertain time delay systems using a novel descriptor redundancy approach based on delay partitioning. First, the original system is casted into an equivalent descriptor singular state–space representation by introducing redundant state variables so that the resulting delay is progressively reduced. From the equivalent model and applying Lyapunov Functional method, a sufficient condition based on Linear Matrix Inequalities (LMIs) for exponential stability with guaranteed decay rate performance is obtained. As a result, the inherent conservatism of Lyapunov–Krasovskii functional techniques can arbitrarily be reduced by increasing the number of delay partition intervals including decay rate performance and model uncertainties in polytopic form. Various benchmark examples are provided to validate the effectiveness of the proposed method, showing better trade-off between conservatism and performance in comparison to previous approaches.

Keywords:

• Exponential stability
• time delay systems
• delay partitioning
• descriptor redundancy
• Lyapunov–Krasovskii functional
• linear matrix inequalities

Acknowledgments

This work was supported by project PGC2018-098719-B-I00 (MCIU/AEI/FEDER,UE).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Given a matrix $W$, we denote $He(W) = W + W^T$.

Additional information

Funding

This work was supported by project PGC2018-098719-B-I00 (MCIU/AEI/FEDER,UE).

Notes on contributors

Antonio González

Antonio González received the Telecommunications Engineer degree in 2001 and his Ph.D. in Automation and Industrial Informatics from Universitat Politècnica de València (UPV) in 2012. He was a postdoctoral researcher at the Laboratory of Industrial and Human Automation control, Mechanical engineering and Computer Science, CNRS, UMR 8201, Valenciennes, France from 2013 to 2014. Currently he works as Associate Professor at the Department of System Engineering and Automation at the Universitat Politècnica de València (Spain). His research interests are within the broad area of time delay systems, robust control, networked control systems, multirobot systems and process control applications.