Exponential stability of time-delay systems with nonlinear uncertainties

Abstract

The global exponential stability and the exponential convergence rate for time-delay systems with nonlinear uncertainties are investigated. A novel exponential stability criterion for the system is derived using the Lyapunov method. These stability conditions are formulated as linear matrix inequalities (LMIs), which can be easily solved by various convex optimization algorithms. The issue of exponential stability for time-delay systems with nonlinear uncertainties using generalized eigen value problem (GEVP) approach remains open, which motivates this paper. Numerical examples are given to illustrate the usefulness of our proposed method.

Keywords:

• exponential stability
• linear matrix inequality
• Lyapunov method
• nonlinear uncertainty
• time-delay systems

2000 AMS Subject Classification: :

• 34K20
• 34D20
• 34A34

Acknowledgement

The work of the authors was supported by the UGC-SAP (DRS) grant.