This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, a delay-dependent stabilizability condition which is expressed in terms of Linear Matrix Inequalities (LMIs) is derived to ensure the closed-loop system is exponentially stable with a prescribed α-convergence rate. The design of an observerbased output feedback controller can be carried out in a systematic and computationally efficient manner via the use of an LMI-based algorithm. A numerical example is given to illustrate the design procedure.
Baser, U. and Kizilsac, B. (2007). Dynamic output feedback H∞ control problem for linear neutral systems, IEEE Transactions on Automatic Control 52(6): 1113-1118.
Blizorukova, M., Kappel, F. and Maksimov, V. (2001). A problem of robust control of a system with time delay, International Journal of Applied Mathematics and Computer Science 11(4): 821-834.
Botmart, T., Niamsup, P. and Phat, V.N. (2011). Delay-dependent exponential stabilization for uncertain linear systems with interval non-differentiable time-varying delays, Applied Mathematics and Computation 217(21): 8236-8247.
Busłowicz, M. (2010). Robust stability of positive continuous-time linear systems with delays, International Journal of Applied Mathematics and Computer Science 20(4): 665-670, DOI: 10.2478/v10006-010-0049-8.
Chen, J.D. (2007). Robust H∞output dynamic observer-based control design of uncertain neutral systems, Journal of Optimization Theory and Applications 132(1): 193-211.
Fridman, E. and Shaked, U. (2002). A descriptor system approach to H∞control of linear time-delay systems, IEEE Transactions on Automatic Control 47(2): 253-270.
Gu, K., Kharitonov, V. L. and Chen, J. (2003). Stability of Time-Delay Systems, Birkhauser, Boston, MA.
Ivanescu, D., Dion, J.M., Dugard, L. and Niculescu, S.I. (2000). Dynamical compensation for time-delay systems: An LMI approach, International Journal of Robust and Nonlinear Control 10(8): 611-628.
Kaczorek, T. and Busłowicz, M. (2004). Minimal realization for positive multivariable linear systems with delay, International Journal of Applied Mathematics and Computer Science 14(2): 181-187.
Kowalewski, A. (2009). Time-optimal control of infinite order hyperbolic systems with time delays, International Journal of Applied Mathematics and Computer Science 19(4): 597-608, DOI: 10.2478/v10006-009-0047-x.
Kwon, O.M., Park, J.H., Lee, S.M. and Won, S.C. (2006). LMI optimization approach to observer-based controller design of uncertain time-delay systems via delayed feedback, Journal of Optimization Theory and Applications 128(1): 103-117.
Park, J.H. (2004). On the design of observer-based controller of linear neutral delay-differential systems, Applied Mathematics and Computation 150(1): 195-202.
Park, P. (1999). A delay-dependent stability criterion for systems with uncertain time-invariant delays, IEEE Transactions on Automatic Control 44(4): 876-877.
Phat, V.N., Khongtham, Y. and Ratchagit, K. (2012). LMI approach to exponential stability of linear systems with interval time-varying delays, Linear Algebra and Its Applications 436(1): 243-251.
Raja, R., Sakthivel, R., Anthoni, S.M. and Kim, H. (2011). Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delays, International Journal of Applied Mathematics and Computer Science 21(1): 127-135, DOI: 10.2478/v10006-011-0009-y.
Richard, J.P. (2003). Time-delay systems: An overview of some recent advances and open problems, Automatica 39(10): 1667-1694.
Shao, H. (2009). New delay-dependent stability criteria for systems with interval delay, Automatica 45(3): 744-749.
Shao, H. and Han, Q.L. (2012). Less conservative delay-dependent stability criteria for linear systems with interval time-varying delays, International Journal of Systems Science 43(5): 894-902.
Tokarzewski, J. (2009). Zeros in linear systems with time delay in state, International Journal of Applied Mathematics and Computer Science 19(4): 609-617, DOI: 10.2478/v10006-009-0048-9.
Tong, S., Yang, G. and Zhang, W. (2011). Observer-based fault-tolerant control against sensor failures for fuzzy systems with time delays, International Journal of Applied Mathematics and Computer Science 21(4): 617-627, DOI: 10.2478/v10006-011-0048-4.
Trinh, H. (1999). Linear functional state observer for time-delay systems, International Journal of Control 72(18): 1642-1658.
Trinh, H. and Aldeen, M. (1994). Stabilization of uncertain dynamic delay systems by memoryless feedback controllers, International Journal of Control 59(6): 1525-1542.
Trinh, H. and Aldeen, M. (1997). On robustness and stabilization of linear systems with delayed nonlinear perturbations, IEEE Transactions on Automatic Control 42(7): 1005-1007.
Trinh, H.M., Teh, P.S. and Fernando, T.L. (2010). Time-delay systems: Design of delay-free and low-order observers, IEEE Transactions on Automatic Control 55(10): 2434-2438.
Xiang, Z., Wang, R. and Chen, Q. (2010). Fault tolerant control of switched nonlinear systems with time delay under asynchronous switching, International Journal of Applied Mathematics and Computer Science 20(3): 497-506, DOI: 10.2478/v10006-010-0036-0.