New stability conditions for nonlinear time varying delay systems

Abstract

In this paper, new practical stability conditions for a class of nonlinear time varying delay systems are proposed. The study is based on the use of a specific state space description, known as the Benrejeb characteristic arrow form matrix, and aggregation techniques to obtain delay-dependent stability conditions. Application of this method to delayed Lurie–Postnikov nonlinear systems is given. Illustrative examples are presented to show the effectiveness of the proposed approach.

Keywords:

• nonlinear time delay systems
• stability analysis
• delay-dependent stability
• arrow matrix
• Lurie–Postnikov systems

Additional information

Notes on contributors

S. Elmadssia

Sami Elmadssia received his engineering diploma in electrical engineering in 2004 and master's diploma in automatic treatment of signals in 2005. In 2011, he received his PhD from the National School of Engineers of Tunis (ENIT), Tunisia. Presently, he is a researcher at the research unit LARA Automatique of ENIT. His research interests include stability and control of linear and nonlinear time delay systems and applications to process control problems.

K. Saadaoui

Karim Saadaoui received his PhD at the Electrical and Electronics Engineering Department of the University of Bilkent of Ankara in 2003. He is a researcher at the research laboratory LARA Automatique of the National Engineering School of Tunis (ENIT), Tunisia. His research interests are in the areas of time delay systems, stability robustness and applications of robust control to process control problems.

M. Benrejeb

Mohamed Benrejeb received his PhD degree in 1976 from the University of Sciences and Technologies in Lille (France). He also obtained a French State Doctorate in 1980 from the same university. He has been working as a full professor with ENIT since 1985. His main scientific interests include analysis and synthesis of complex systems (stability, stabilisability, automatic control by classic and non-conventional methods, using fuzzy logic, neural network, neuro-fuzzy) and optimisation with scheduling by evolutionary approaches.