This paper studies the stability conditions of a discrete-time switched linear system in the presence of affine parametric uncertainties and an unknown time delay. Based on a discrete Lyapunov functional, sufficient conditions are investigated to determine the upper bound of admissible time delay in the discrete-time switched system. Furthermore, the average dwell time method, which is an effective tool for stability analysis of switched systems, is used to derive the exponential stability conditions. These conditions characterize the switching signal, which does not depend on any uncertainties. Finally, numerical examples are provided to verify and compare the theoretical results.
BinazadehTBahmaniM (2016a) Design of robust controller for a class of uncertain discrete-time systems subject to actuator saturation. IEEE Transactions on Automatic Control. DOI: 10.1109/TAC.2016.2580662
2.
BinazadehTBahmaniM (2016b) Robust time-varying output tracking control in the presence of actuator saturation. Transactions of the Institute of Measurement and Control, 0142331216650022.
3.
BinazadehTShafieiMH (2013) Output tracking of uncertain fractional-order nonlinear systems via a novel fractional-order sliding mode approach. Mechatronics23(7): 888–892.
4.
BinazadehTShafieiMH (2014) Robust stabilization of uncertain nonlinear slowly-varying systems: application in a time-varying inertia pendulum. ISA Transactions53(2): 373–379.
5.
BoydSGhaouiLEFeronE. (1994) Linear matrix inequalities in system and control theory. SIAM Studies in Applied Mathematics, Vol. 15.
6.
ChenJDWuITLienCH. (2014) Robust exponential stability for uncertain discrete-time switched systems with interval time-varying delay through a switching signal. Journal of Applied Research and Technology12(6): 1187–1197.
7.
DonkersMHeemelsWWouwandN. (2011) Stability analysis of networked control systems using a switched linear systems approach. IEEE Transactions on Automatic Control56(9): 2101–2115.
8.
HespanhaJPMorseAS (1999) Stability of switched systems with average dwell-time. In: Proceedings of the 38th IEEE Conference on Decision Control, pp. 2655–2660.
9.
KermaniMSaklyA (2014) On stability analysis of discrete-time uncertain switched nonlinear time-delay systems. Advances in Difference Equations2014(1): 1–22.
10.
KimSCampbellSALiuXZ (2006) Stability of a class of linear switching systems with time delay. IEEE Transactions on Circuits and Systems53(2): 384–393.
11.
LiberzonD (2003) Switching in Systems and Control. Boston, MA: Birkhauser.
12.
LiberzonDMorseAS (1999) Basic problems in stability and design of switched systems. IEEE Control Systems Magazine19(5): 59–70.
13.
LiberzonDTempoR (2004) Common Lyapunov functions and gradient algorithms. IEEE Transactions on Automatic Control49(6): 990–994.
14.
LinHAntsaklisPJ (2009) Stability and stabilizability of switched linear systems: a survey of recent results. IEEE Transactions on Automatic Control45(2): 308–322.
15.
LiuJLiuXXieWC (2008) Delay-dependent robust control for uncertain switched systems with time-delay. Nonlinear Analysis: Hybrid Systems2(1): 81–95.
16.
MeyerCD (2000) Matrix Analysis and Applied Linear Algebra. Philadelphia, PA: SIAM.
17.
NiamsupPRajchakitP (2013) New results on robust stability and stabilization of linear discrete-time stochastic systems with convex polytopic uncertainties. Journal of Applied Mathematics. DOI: 10.1155/2013/368259
18.
OishiMTomlinC (1999) Switched nonlinear control of a VSTOL aircraft. In: Proceedings of the 38th IEEE Conference on Decision and Control, pp. 2685–2690.
19.
PetterssonSLennartsonB (2000) Stability of hybrid systems using LMIs: a gear-box application. Hybrid Systems: Computation and Control. Berlin: Springer, pp. 381–395.
20.
PhatVN (2005) Robust stability and stabilizability of uncertain linear hybrid systems with state delays. IEEE Transactions on Circuits Systems II – Express Briefs52(2): 94–98.
21.
PhatVNRatchagitK (2011) Stability and stabilization of switched linear discrete-time systems with interval time-varying delay. Nonlinear Analysis: Hybrid Systems5(4): 605–612.
22.
RajchakitG (2012a) Robust stability and stabilization of uncertain switched discrete-time systems. Advances in Difference Equations2012(1): 1–15.
23.
RajchakitG (2012b) Robust stability and stabilization of nonlinear uncertain stochastic switched discrete-time systems with interval time-varying delays. Applied Mathematics & Information Sciences6: 555–565.
24.
RajchakitG (2013) Switching design for the asymptotic stability and stabilization of nonlinear uncertain stochastic discrete-time systems. International Journal of Nonlinear Sciences and Numerical Simulation14(1): 33–44.
25.
RajchakitG (2014a) Stabilization of switched discrete-time systems with convex polytopic uncertainties. Journal of Computational Analysis and Applications16(1): pp. 20–29.
26.
RajchakitG (2014b) Switching design for the robust stability of nonlinear uncertain stochastic switched discrete-time systems with interval time-varying delay. Journal of Computational Analysis & Applications16(1): 10–19.
27.
RajchakitMRajchakitG (2012) Mean square robust stability of stochastic switched discrete-time systems with convex polytopic uncertainties. Journal of Inequalities and Applications2012: 135. DOI: 10.1186/1029-242X-2012-135.
28.
RajchakitMRajchakitG (2013) New delay-dependent sufficient conditions for the exponential stability of linear hybrid systems with interval time-varying delays. In: Third World Congress on Information and Communication Technologies (WICT), pp. 230–233.
29.
RajchakitMNiamsupPRajchakitG (2013) A constructive way to design a switching rule and switching regions to mean square exponential stability of switched stochastic systems with non-differentiable and interval time-varying delay. Journal of Inequalities and Applications1: 1–14.
30.
SchererCWeilandS (2005) Linear matrix inequalities in control. Technical report, Delft Center for Systems and Control, Delft University of Technology.
31.
SongYFanJFeiM. (2008) Robust H∞ control of discrete switched system with time delay. Applied Mathematics and Computation205(1): 159–169.
32.
SunYGWangLXieG (2006) Delay-dependent robust stability and stabilization for discrete-time switched systems with mode-dependent time-varying delays. Applied Mathematics and Computation180(2): 428–435.
33.
SunZGeSS (2005) Switched Linear Systems: Control and Design. New York: Springer.
34.
WuMHeYSheJH (2010) Stability Analysis and Robust Control of Time-delay Systems. Beijing/Berlin: Science Press/Springer.
35.
YanPOzbayH (2008) Stability analysis of switched time delay systems. SIAM Journal on Control and Optimization47(2): 936–949.
36.
ZhangLBoukasEKShiP (2008) Exponential H∞ filtering for uncertain discrete-time switched linear systems with average dwell time: a μ-dependent approach. International Journal of Robust and Nonlinear Control18: 1188–1207.
ZhangYYanP (2015) Delay-dependent stability analysis for uncertain switched time-delay systems using average dwell time. Mathematical Problems in Engineering2015. DOI: 10.1155/2015/628693.
