zbMATH — the first resource for mathematics

Delay-dependent state feedback stabilization for a networked control model with two additive input delays. (English) Zbl 1410.93097
Summary: This paper is centered on delay-dependent state feedback stabilization for a networked control model with two additive input delays. Firstly delay-dependent stability is investigated. By splitting the whole delay interval into subintervals according to the delays, a Lyapunov functional is constructed. To reduce conservatism we handle the Lyapunov functional in two ways. More specifically, we take the Lyapunov functional as a whole to examine its positive definite, rather than restrict each term of it to positive definite as usual. In addition, when estimating the derivative of the Lyapunov functional, we manage to get a fairly tighter upper bound by introducing different slack variables for the different subintervals. The resulting stability results turn out dependent on the two delays separately, and less conservative than some existing ones. Then, based on the stability results state feedback stabilization is studied. Delay-dependent conditions are formulated for the controller such that the closed-loop system is asymptotically stable. Finally examples are given to show the less conservatism of the stability results and the effectiveness of the proposed stabilization method.

MSC:
 93D15 Stabilization of systems by feedback 93C23 Control/observation systems governed by functional-differential equations
Full Text:
References:
 [1] Wang, G., Partially mode-dependent design of H^∞ filter for stochastic Markovian jump systems with mode-dependent time delays, J. Math. Anal. Appl., 383, 2, 573-584, (2011) · Zbl 1219.93134 [2] Gu, K.; Kharitonov, V. L.; Chen, J., Stability of time-delay systems, (2003), Birkhäuser Boston · Zbl 1039.34067 [3] Peng, C.; Yang, T., Event-triggered communication and H^∞ control co-design for networked control systems, Automatica, 49, 1326-1332, (2013) · Zbl 1319.93022 [4] Zhang, X. M.; Han, Q.-L., Event-triggered dynamic output feedback control for networked control systems, IET Control Theory and Appl., 8, 4, 226-234, (2014) [5] Li, T.; Guo, L.; Sun, C.; Lin, C., Further results on delay-dependent stability criteria of neural networks with time-varying delays, IEEE Trans. on Neural netw., 19, 4, 726-730, (2008) [6] Jiang, X.; Han, Q.-L; Liu, S.; Xue, A., A new H_∞ stabilization criterion for networked control systems, IEEE Trans. Automat. Control, 53, 1025-1032, (2008) · Zbl 1367.93179 [7] Zhu, X. L.; Yang, G. H., New results of stability analysis for systems with time-varying delay, Int. J. Robust and Nonlinear Control, 20, 5, 596-606, (2010) · Zbl 1185.93112 [8] Zhu, X. L.; Wang, Y.; Yang, G. H., New stability criteria for continuous-time systems with interval time-varying delay, IET Control Theory and Appl., 4, 6, 1101-1107, (2010) [9] Xu, S.; Lam, J., Improved delay-dependent stability criteria for time-delay systems, IEEE Trans. Automat. Control, 50, 384-387, (2005) · Zbl 1365.93376 [10] Xu, S.; Lam, J.; Zou, Y., An improved characterization of bounded realness for singular delay systems and its applications, Int. J. Robust and Nonlinear Control, 18, 3, 263-277, (2008) · Zbl 1284.93117 [11] He, Y.; Wang, Q.; Lin, C.; Wu, M., Delay-range-dependent stability for systems with time-varying delay, Automatica, 43, 371-376, (2007) · Zbl 1111.93073 [12] Shao, H., Improved delay-dependent stability criteria for systems with a delay in a range, Automatica, 44, 12, 3215-3218, (2008) · Zbl 1153.93476 [13] Shao, H., New delay-dependent stability criteria for systems with interval time-varying delay, Automatica, 45, 3, 744-749, (2009) · Zbl 1168.93387 [14] Lam, J.; Gao, H.; Wang, C., Stability analysis for continuous systems with two additive time-varying delay component, Sys. Control Lett., 56, 16-24, (2007) · Zbl 1120.93362 [15] Gao, H.; Chen, T.; Lam, J., A new delay system approach to network-based control, Automatica, 44, 39-52, (2008) · Zbl 1138.93375 [16] Li, P., Further results on delay-range-dependent stability with additive time-varying delay systems, ISA Trans., 53, 258-266, (2014) [17] H. Shao, Z. Zhang, X. Zhu, G. Miao, H^∞ control for a networked control model of systems with two additive time-varying delays, Abstract and Applied Analysis Article ID 923436 (2014). http://dx.doi.org/10.1155/2014/923436. [18] Ge, X., Comments and an improved result on “stability analysis for continuous system with additive time-varying delays: a less conservative result”, Appl. Math. Comput., 241, 42-46, (2014) · Zbl 1334.34161 [19] Gu, K., An integral inequality in the stability problem of time-delay systems, (Proceedings of 39th IEEE conference on decision and control, Sydney, Australia, (2000)), 2805-2810, December [20] Ghaoui, L. E.; Oustry, F.; Rami, M. A., A cone complementarity linearization algorithm for static output-feedback and related problems, IEEE Trans. Automat. Control, 42, 1171-1176, (1997) · Zbl 0887.93017 [21] Han, Q. L., A discrete delay decomposition approach to stability of linear retarded and neutral systems, Automatica, 45, 517-524, (2009) · Zbl 1158.93385 [22] Shen, H.; Xu, S.; Lu, J.; Zhou, J., Passivity-based control for uncertain stochastic jumping systems with mode-dependent round-trip time delays, J. Franklin Inst., 349, 1665-1680, (2012) · Zbl 1254.93148 [23] Shen, H.; Park, J. H.; Wu, Z., Reliable mixed passive and H^∞ filtering for semi-Markov jump systems with randomly occurring uncertainties and sensor failures, Int. J. Robust Nonlinear Control, (2014) [24] Shen, H.; Park, J. H.; Zhang, L.; Wu, Z. G., Robust extended dissipative control for sampled-data Markov jump systems, Int. J. Control, 87, 1549-1564, (2014) · Zbl 1317.93171
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.