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On the Codimension of the Singularity at the Origin for Networked Delay Systems Read chapter Read first chapter

2016 | OriginalPaper | Chapter

6. On the Stability Analysis of Sampled-Data Systems with Delays

Authors : Alexandre Seuret, Corentin Briat

Published in: Delays and Networked Control Systems

Publisher: Springer International Publishing

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Abstract

Controlling a system through a network amounts to solve certain difficulties such as, among others, the consideration of aperiodic sampling schemes and (time-varying) delays. In most of the existing works, delays have been involved in the input channel through which the system is controlled, thereby delaying in a continuous way the control input computed by the controller. We consider here a different setup where the delay acts in a way that the current control input depends on past state samples, possibly including the current one, which is equivalent to considering a discrete-time delay, at the sample level, in the feedback loop. An approach based on the combination of a discrete-time Lyapunov–Krasovskii functional and a looped-functional is proposed and used to obtain tailored stability conditions that explicitly consider the presence of delays and the aperiodic nature of the sampling events. The stability conditions are expressed in terms of linear matrix inequalities and the efficiency of the approach is illustrated on an academic example.

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previous chapter Analysis of Bilinear Systems with Sampled-Data State Feedback
next chapter Output Feedback Event-Triggered Control
Literature
1.
Y. Ariba, C. Briat, K.H. Johansson, Simple conditions for \({L_2}\) stability and stabilization of networked control systems, in IFAC World Congress, 2011
2.
C. Briat, Convergence and equivalence results for the Jensen’s inequality: application to time-delay and sampled-data systems. IEEE Trans. Autom. Control 56(7), 1660–1665 (2011)MathSciNetCrossRef
3.
C. Briat, Convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled-data systems under dwell-time constraints. Automatica 49(11), 3449–3457 (2013)MathSciNetCrossRefMATH
4.
C. Briat, Convex conditions for robust stabilization of uncertain switched systems with guaranteed minimum and mode-dependent dwell-time. Syst. Control Lett. 78, 63–72 (2015)MathSciNetCrossRefMATH
5.
C. Briat, Linear Parameter-Varying and Time-Delay Systems—Analysis, Observation, Filtering and Control. Advances on Delays and Dynamics, vol. 3 (Springer, Heidelberg, 2015)
6.
C. Briat, Theoretical and numerical comparisons of looped functionals and clock-dependent Lyapunov functions—the case of periodic and pseudo-periodic systems with impulses. Int. J. Robust Nonlinear Control (2016) (to appear)
7.
C. Briat, A. Seuret, Convex dwell-time characterizations for uncertain linear impulsive systems. IEEE Trans. Autom. Control 57(12), 3241–3246 (2012)MathSciNetCrossRef
8.
C. Briat, A. Seuret, A looped-functional approach for robust stability analysis of linear impulsive systems. Syst. Control Lett. 61(10), 980–988 (2012)MathSciNetCrossRefMATH
9.
T. Chen, B.A. Francis, Optimal Sampled-Data Control Systems (Springer, 1995)
10.
M.B.G. Cloosterman, N. van de Wouw, W.P.M.H. Heemels, H. Nijmeijer, Stability of networked control systems with uncertain time-varying delays. IEEE Trans. Autom. Control 54(7), 1575–1580 (2009)MathSciNetCrossRef
11.
12.
E. Fridman, A. Seuret, J.-P. Richard, Robust sampled-data stabilization of linear systems: an input delay approach. Automatica 40(8), 1141–1446 (2004)MathSciNetCrossRefMATH
13.
E. Fridman, U. Shaked, Stability and guaranteed cost control of uncertain discrete delay systems. Int. J. Control 78(4), 235–246 (2005)MathSciNetCrossRefMATH
14.
15.
W.P.M.H. Heemels, A.R. Teel, N. van de Wouw, D. Nesic, Networked control systems with communication constraints: tradeoffs between transmission intervals, delays and performance. IEEE Trans. Autom. Control 55(8), 1781–1796 (2010)MathSciNetCrossRef
16.
J.P. Hespanha, P. Naghshtabrizi, Y. Xu, A survey of recent results in networked control systems. Proc. IEEE 95(1), 138–162 (2007)CrossRef
17.
L. Hetel, J. Daafouz, C. Iung, Stabilization of arbitrary switched linear systems with unknown time-varying delays. IEEE Trans. Autom. Control 51(10), 1668–1674 (2006)MathSciNetCrossRef
18.
C.-Y. Kao, H. Fujioka, On stability of systems with aperiodic sampling devices. IEEE Trans. Autom. Control 58(3), 2085–2090 (2013)MathSciNetCrossRef
19.
C.-Y. Kao, D.-R. Wu, On robust stability of aperiodic sampled-data systems: an integral quadratic constraint approach, in IEEE American Control Conference (ACC), 2014
20.
K. Liu, E. Fridman, Discontinuous Lyapunov functionals for linear systems with sawtooth delays, in IFAC Workshop on Time-Delay Systems (TDS), 2009
21.
K. Liu, E. Fridman, Networked-based stabilization via discontinuous Lyapunov functionals. Int. J. Robust Nonlinear Control 22(4), 420–436 (2012)MathSciNetCrossRefMATH
22.
23.
R.H. Middleton, G.C. Goodwin, Digital Control and Estimation: A Unified Approach (Prentice-Hall, 1990)
24.
L. Mirkin, Some remarks on the use of time-varying delay to model sample-and-hold circuits. IEEE Trans. Autom. Control 52(6), 1009–1112 (2007)MathSciNetCrossRef
25.
P. Naghshtabrizi, J.P. Hespanha, A.R. Teel, Exponential stability of impulsive systems with application to uncertain sampled-data systems. Syst. Control Lett. 57(5), 378–385 (2008)MathSciNetCrossRefMATH
26.
P. Naghshtabrizi, J.P. Hespanha, A.R. Teel, Stability of delay impulsive systems with application to networked control systems. Trans. Inst. Meas. Control 32(5), 511–528 (2010)CrossRef
27.
Y. Oishi, H. Fujioka, Stability and stabilization of aperiodic sampled-data control systems: an approach using robust linear matrix inequalities, in Joint IEEE Conference on Decision and Control and Chinese Control Conference (CDC-CCC), 2009
28.
P.G. Park, J.W. Ko, C. Jeong, Reciprocally convex approach to stability of systems with time-varying delays. Automatica 47(1), 235–238 (2011)MathSciNetCrossRefMATH
29.
A. Seuret, Stability analysis for sampled-data systems with a time-varying period, in Joint IEEE Conference on Decision and Control and Chinese Control Conference (CDC-CCC), 2009
30.
A. Seuret, Stability analysis of networked control systems with asynchronous sampling and input delay, in IEEE American Control Conference (ACC), 2011
31.
32.
A. Seuret, C. Briat, Stability analysis of uncertain sampled-data systems with incremental delay using looped-functionals. Automatica 55, 274–278 (2015)MathSciNetCrossRefMATH
33.
A. Seuret, C. Briat, F. Gouaisbaut. Stability analysis of asynchronous sampled-data systems with discrete-time constant input delay, in IEEE Conference on Decision and Control (CDC), 2014
34.
A. Seuret, F. Gouaisbaut, Wirtinger-based integral inequality: application to time-delay systems. Automatica 49(9), 2860–2866 (2013)MathSciNetCrossRef
35.
36.
S. Xu, J. Lam, C. Yang, Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay. Syst. Control Lett. 43(2), 77–84 (2001)MathSciNetCrossRefMATH
37.
Y. Yamamoto, New approach to sampled-data control systems: a function space method, in IEEE Conference on Decision and Control (CDC), 1990
38.
S. Zampieri, A survey of recent results in networked control systems, in IFAC World Congress, 2008
39.
W. Zhang, M.S. Branicky, S.M. Phillips, Stability of networked control cystems. IEEE Control Syst. Mag. 21(1), 84–99 (2001)CrossRef
Metadata
Title
On the Stability Analysis of Sampled-Data Systems with Delays
Authors
Alexandre Seuret
Corentin Briat
Copyright Year
2016
Book
Delays and Networked Control Systems

Print ISBN: 978-3-319-32371-8

Electronic ISBN: 978-3-319-32372-5

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-32372-5_6