The problem of adaptive finite-time control is addressed in this paper for a class of non-linear delay systems. First, the concepts of adaptive finite-time stability and adaptive finite-time boundedness are defined, respectively. Then, by resorting to the Lyapunov–Krasovskii functional technique, some new delay-dependent criteria guaranteeing adaptive finite-time boundedness and adaptive finite-time stability are developed, respectively. An explicit expression for the desired non-fragile state feedback controller is also presented. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed results.
AmatoFAriolaM (2005) Finite-time control of discrete-time linear systems. IEEE Transactions on Automatic Control50(5): 724–729.
2.
AmatoFAriolaMAbdallahCTDoratoP (1999) Finite-time control for uncertain linear systems with disturbance input. In: American control conference, San Diego, USA, 2–4 June 1999, pp. 1776–1780. Piscataway, NJ: IEEE.
3.
AmatoFAriolaMCosentinoC (2006) Finite-time stabilization via dynamic output feedback. Automatica42(2): 337–342.
4.
AmatoFAriolaMDoratoP (2001) Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica37(9): 1459–1463.
5.
DoratoP (1961) Short time stability in linear time-varying systems. In: IRE international convention, New York, USA, 20–23 March 1961, pp. 83–87. Athens, OH: Institute of Radio Engineers.
6.
DuHBLinXZLiSH (2009) Finite-time stability and stabilization of switched linear systems. In: 48th IEEE conference on decision and control, Shanghai, China, 15–18 Dec 2009, pp. 1938–1943. Piscataway, NJ: IEEE.
7.
FengJWuZSunJ (2005) Finite-time control of linear singular systems with parametric uncertainties and disturbances. Acta Automatica Sinica31(14): 634–637.
8.
GhaouiELOustryFAitRamiM (1997) A cone complementarity linearization algorithm for static output feedback and related problems. IEEE Transactions on Automatic Control42(8): 1171–1176.
9.
HouLLZongGDWuYQ (2012a) Finite-time control for switched delay systems via dynamic output feedback. International Journal of Innovative Computing, Information and Control8(7): 4901–4913.
10.
HouLLZongGDWuYQ (2012b) Finite-time control for discrete-time switched systems with time delay. International Journal of Control, Automation, and Systems10(4): 855–860.
11.
HuHJiangBYangH (2013) Non-fragile H2 reliable control for switched linear systems with actuator faults. Signal Processing93(7): 1804–1812.
12.
LiuYHNiuYGZouYY (2014) Non-fragile observer-based sliding mode control for a class of uncertain switched systems. Journal of the Franklin Institute351(2): 952–963.
13.
PetersenIRHollotCV (1986) A Riccati equation approach to the stabilization of uncertain linear systems. Automatica22(4): 397–411.
14.
WangDWangWShiP (2009a) Delay-dependent exponential stability for switched delay systems. Optimal Control Applications and Methods30(4): 383–397.
15.
WangDWangWShiP (2009b) Robust fault detection for switched linear systems with state delays. IEEE Transactions on Systems, Man and Cybernetics, Part B: Cybernetics39(3): 800–805.
16.
WangDWangWShiP (2009c) Exponential H∞ filtering for switched linear systems with interval time-varying delay. International Journal of Robust and Nonlinear Control19(5): 532–551.
17.
WuLGQiTFengZ (2009) Average dwell time approach to L2−L∞ control of switched delay systems via dynamic output feedback. IET Control Theory and Applications3(10): 1425–1436.
ZongGDHouLLLiJF (2011) A descriptor system approach to l2−l∞ filtering for uncertain discrete-time switched systems with mode-dependent time-varying delays. International Journal of Innovative Computing, Information and Control7(5): 2213–2224.
20.
ZongGDHouLLYangHY (2009) Further results concerning delay-dependent H∞ control for uncertain discrete-time systems with time-varying delay. Mathematical Problems in Engineering2009: 732181.
21.
ZongGDXuSYWuYQ (2008) Robust H∞ stabilization for uncertain switched impulsive control systems with state delay: An LMI approach. Nonlinear Analysis: Hybrid Systems2(4): 1287–1300.
