On computing maximum allowable time delay of Lur’e systems with uncertain time-invariant delays
- 125 Downloads
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.
KeywordsAbsolute stability criterion delay-dependent linear matrix inequality (LMI) Lur’e systems Lyapunov-Krasovskii functional time-invariant delays
Unable to display preview. Download preview PDF.
- J. E. Normey-Rico and E. F. Camacho, Control of Dead-time Processes, Springer, 2007.Google Scholar
- L. Yu, Q. L. Han, S. Yu, and J. Gao, “Delaydependent conditions for robust absolute stability of uncertain time-delay systems,” Proc. of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, USA, pp. 6033–6037, 2003.Google Scholar
- F. Gouaisbaut and D. Peaucelle, “Delay-dependent robust stability of time delay systems,” Proc. of the 5th IFAC Symposium on Robust Control Design, Toulouse, France, pp. 453–458, 2006.Google Scholar
- Q. L. Han, “A delay decomposition approach to stability of linear neutral system,” Proc. of the 17th IFAC World Congress, Seoul, Korea, pp. 2607–2612, 2008.Google Scholar
- S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15 of Studies in Applied Mathematics, SIAM, Philadelphia, PA, 1994.Google Scholar
- Y. Nesterov and A. Nemirovski, Interior-point Polynomial Methods in Convex Programming, vol. 13 of Studies in Applied Mathematics, SIAM, Philadelphia, PA, 1994.Google Scholar
- P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox, Math Works, MA, 1995.Google Scholar