The stability problem of nonlinear time-delay systems is addressed. A quadratic constraint is employed to exploit the structure of nonlinearity in dynamical systems via a set of multiplier matrices. This yields less conservative results concerning stability analysis. By employing a Wirtinger-based inequality, a delay-dependent stability criterion is derived in terms of linear matrix inequalities for the nominal and uncertain systems. A numerical example is used to demonstrate the effectiveness of the proposed stability conditions in dealing with some larger class of nonlinearities.
AcikmeseBCorlessM (2008) Stability analysis with quadratic Lyapunov functions: Some necessary and sufficient multiplier conditions. Systems and Control Letters57(1): 78–94.
2.
AcikmeseBCorlessM (2011) Observers for systems with nonlinearities satisfying incremental quadratic constraints. Automatica47(7): 1339–1348.
3.
BriatC (2011) Convergence and equivalence results for the Jensen’s inequality-application to time-delay and sampled-data systems. IEEE Transactions on Automatic Control56(7): 1660–1665.
4.
DuanWDuBYouJ. (2015) Improved robust stability criteria for a class of Lure systems with interval time-varying delays and sector-bounded nonlinearity. International Journal of Systems Science46(5): 944–954.
5.
EkramianMHosseinniaSSheikholeslamF (2011) Observer design for non-linear systems based on a generalised Lipschitz condition. IET Control Theory and Applications5(16): 1813–1818.
6.
EkramianMHosseinniaSSheikholeslamF (2013) General framework in designing Luenberger-like non-linear observer. IET Control Theory and Applications7(2): 253–260.
7.
FridmanE (2014) Tutorial on Lyapunov-based methods for time-delay systems. European Journal of Control20(6): 271–283.
8.
GouaisbautFPeaucelleD (2006) Delay-dependent robust stability of time delay systems. In: Proceedings of the 5th IFAC symposium on robust control design, Toulouse, France, 5–7 July.
9.
GuKKharitonovVLChenJ (2003) Stability of Time-Delay Systems. Boston: Birkhäuser.
10.
HanQL (2005) Absolute stability of time-delay systems with sector-bounded nonlinearity. Automatica41(12): 2171–2176.
11.
HanQL (2008) A new delay-dependent absolute stability criterion for a class of nonlinear neutral systems. Automatica44(1): 272–277.
12.
HeYWuM (2003) Absolute stability for multiple delay general Lure control systems with multiple nonlinearities. Journal of Computational and Applied Mathematics159(2): 241–248.
13.
HeYWuMSheJH. (2005) Robust stability for delay Lure control systems with multiple nonlinearities. Journal of Computational and Applied Mathematics176(2): 371–380.
14.
KarafyllisIMalisoffMMazencF. (2016) Recent Results on Nonlinear Delay Control Systems. Springer International Publishing.
15.
KhalilHKGrizzleJ (1996) Nonlinear Systems. Vol. 3. New Jersey: Prentice Hall.
16.
LiuYLeeSKwonO. (2015) Robust delay-dependent stability criteria for time-varying delayed Lure systems of neutral type. Circuits, Systems, and Signal Processing34(5): 1481–1497.
17.
MajeedRAhmadSRehanM (2015) Delay-range-dependent observer-based control of nonlinear systems under input and output time-delays. Applied Mathematics and Computation262: 145–159.
18.
MoonYSParkPKwonWH. (2001) Delay-dependent robust stabilization of uncertain state-delayed systems. International Journal of Control74(14): 1447–1455.
19.
ParkP (1999) A delay-dependent stability criterion for systems with uncertain time-invariant delays. IEEE Transactions on Automatic Control44(4): 876–877.
20.
RehanMIqbalNHongKS (2016) Delay-range-dependent control of nonlinear time-delay systems under input saturation. International Journal of Robust and Nonlinear Control26(8): 1647–1666.
21.
SeuretAGouaisbautF (2013) Wirtinger-based integral inequality: application to time-delay systems. Automatica49(9): 2860–2866.
22.
TalebiSAtaeiMEkramianM (2016) Guaranteed interval of delay for a class of non-linear control systems. Transactions of the Institute of Measurement and Control38: 364–369.
23.
XieL (1996) Output feedback Hinf control of systems with parameter uncertainty. International Journal of Control63(4): 741–750.
24.
XuSLamJ (2008) A survey of linear matrix inequality techniques in stability analysis of delay systems. International Journal of Systems Science39(12): 1095–1113.
