On computing maximum allowable time delay of Lur’e systems with uncertain time-invariant delays

  • Thapana Nampradit
  • David Banjerdpongchai
Regular Papers Control Theory


In this paper, we present an improved delay-dependent absolute stability criterion for Lur’e systems with time delays. The guarantee of absolute stability is provided by Lyapunov-Krasovskii theorem with the Lyapunov functional containing the integral of sector-bounded nonlinearities. The Lyapunov functional terms involving delay are partitioned to be associated with each equidistant fragment on the length of time delay. Employing the Jensen inequality and S-procedure, the sufficient condition is derived from time derivative of the Lyapunov functional. Then, the absolute stability criterion expressed in terms of linear matrix inequalities (LMIs) can be efficiently solved using available LMI solvers. The bisection method is used to determine the maximum allowable time delays to ensure the stability of Lur’e systems in the presence of uncertain time-invariant delays. In addition, the stability criterion is extended to Lur’e systems subject to norm-bounded uncertainties by using the matrix eliminating lemma. Numerical results from two benchmark problems show that the proposed criteria give significant improvement on the maximum allowable time delays.


Absolute stability criterion delay-dependent linear matrix inequality (LMI) Lur’e systems Lyapunov-Krasovskii functional time-invariant delays 


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Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Electrical Engineering, Faculty of EngineeringChulalongkorn UniversityPathumwan, BangkokThailand

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