## Robust stability of interval time-delay systems with delay-dependence.(English)Zbl 0902.93052

Summary: This paper proposes a sufficient delay-dependent robust stability condition for interval time-delay systems. The properties of the comparison theorem and matrix measures are employed to investigate the problem. The stability criteria are delay-dependent and less conservative than previous delay-independent and delay-dependent stability criteria when the delay is small. Simulation examples are given to demonstrate the application of our result.

### MSC:

 93D09 Robust stability 34K20 Stability theory of functional-differential equations
Full Text:

### References:

 [1] C.T. Chen, S.D. Lin, Delay-dependent stability for uncertain time-delays systems, in: Proc. 1994 R.O.C. Automatic Control Conf., 1994, pp. 308-310. [2] Coppel, W.A., Stability and asymptotic behavior of differential equations, (1965), D.C. Heath Boston, MA · Zbl 0154.09301 [3] Halanay, A., Differential equationoscillation, time lages, (1966), Academic Press New York [4] Hale, J., Theory of functional differential equation, (1977), Springer New York [5] Hmamed, A., Further results on the stability of uncertain time-delay systems, Internat. J. systems sci., 22, 605-614, (1991) · Zbl 0734.93067 [6] Hmamed, A., Further results on the delay-independent asymptotic stability of linear systems, Internat. J. systems sci., 22, 1127-1132, (1991) · Zbl 0733.93064 [7] Kolmanovskii, V.B.; Nosov, V.R., Stability of function differential equation, (1986), Academic Press London · Zbl 0593.34070 [8] Liu, P.L., Robust stability for parametrically perturbed linear systems with time-delay, J. Chinese inst. electrical eng., 1, 191-197, (1994) [9] Lancaster, P., Theory of matrices, (1969), Academic Press New York · Zbl 0186.05301 [10] Lakshmikantham, V.; Leela, S., Differential and integral inequalities, (1969), Academic Press New York · Zbl 0177.12403 [11] Manu, M.Z.; Mohammad, J., Time-delays analysis, optimization and application, (1987), AT&T Bell Laboratories New York [12] Mori, T.; Fukuma, N.; Kuwahara, M., Simple stability criteria for single and composite linear systems with time delays, Internat. J. control, 32, 1175-1184, (1981) · Zbl 0471.93054 [13] Mori, T.; Kokame, H., Stability of $$ẋ(t)=Ax(t)+Bx(t−τ)$$, IEEE trans. automat. control, AC 34, 460-462, (1989) · Zbl 0674.34076 [14] Su, T.J.; Huang, C.G., Estimating the delay time for the stability of linear systems, J. electrical eng., 34, 195-198, (1991) [15] Su, T.J.; Huang, C.G., Robust stability of delay dependence for linear uncertain systems, IEEE trans. automat. control, AC 37, 1656-1659, (1992) · Zbl 0770.93077 [16] Su, T.J.; Kuo, T.S.; Sun, Y.Y., Robust stability for linear time-delay systems with linear parameter perturbations, Internat. J. systems sci., 19, 2123-2129, (1988) · Zbl 0653.93046 [17] Tissir, E.; Hmamed, A., Stability tests of interval time delay systems, Systems control lett., 23, 263-270, (1994) · Zbl 0815.93061
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.