×

Stability and stabilization of nonuniform sampling systems. (English) Zbl 1153.93450

Summary: This paper is concerned with nonuniform sampling systems, where the sampling interval is time-varying within a certain known bound. The system is transformed into a time-varying discrete time system, where time-varying parts due to the sampling interval variation are treated as norm bounded uncertainties using robust control techniques. To reduce conservatism arising from modeling time-varying parts as a single uncertainty, the time-varying parts are modeled as \(N\) uncertainties. With larger \(N\), a less conservative stability condition is derived at a sacrifice of more computation. It is shown through a numerical example that the proposed stability condition is better than existing stability conditions.

MSC:

93C57 Sampled-data control/observation systems
93C15 Control/observation systems governed by ordinary differential equations
93D09 Robust stability
93C05 Linear systems in control theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bernstein, Dennis S., Matrix mathematics: Thoery, facts, and formulas with application to linear system theory (2005), Princeton University Press: Princeton University Press Princeton, NJ · Zbl 1075.15001
[2] Boyd, Stephen; El Ghaoui, Laurent; Feron, Eric; Balakrishnan, Venkataramanan, Linear matrix inequalities in system and control theory (1994), Society for Industrial and Applied Mathematics: Society for Industrial and Applied Mathematics Philadelphia · Zbl 0816.93004
[3] Chen, Tongwen; Francis, Bruce, Optimal sampled-data control systems (1995), Springer-Verlag: Springer-Verlag Tokyo · Zbl 0847.93040
[4] Franklin, Gene F.; David Powell, J.; Workman, Michael, Digital control of dynamic systems (1997), Addison Wesley Longman: Addison Wesley Longman Menlo Park · Zbl 0697.93002
[5] Fridman, E.; Seuret, Alexandre; Richard, Jean-Pierre, Robust sampled-data stabilization of linear systems: An input delay approach, Automatica, 40, 1441-1446 (2004) · Zbl 1072.93018
[6] Fujioka, Hisaya (2008). Stability analysis for a class of networked/embedded control systems: A discrete-time approach. In Proceedings of American control conference; Fujioka, Hisaya (2008). Stability analysis for a class of networked/embedded control systems: A discrete-time approach. In Proceedings of American control conference
[7] Hu, Li-Sheng; Bai, Tao; Shi, Peng; Wu, Ziming, Sampled-data control of networked linear control systems, Automatica, 43, 903-911 (2007) · Zbl 1117.93044
[8] Khalil, Hassan K., Nonlinear systems (1996), Prentice-Hall: Prentice-Hall New Jersey · Zbl 0842.93033
[9] Mirkin, Leonid, Some remarks on the use of time-varying delay to model sample-and-hold circuits, IEEE Transactions on Automatic Control, 52, 6, 1109-1112 (2007) · Zbl 1366.94798
[10] Naghshtabrizi, Payam, Hespanha, Joao P., & Teel, Andrew R. (2006). On the robust stability and stabilization of sampled-data systems: A hybrid system approach. In Proc. of the 45th IEEE conference on decision and control; Naghshtabrizi, Payam, Hespanha, Joao P., & Teel, Andrew R. (2006). On the robust stability and stabilization of sampled-data systems: A hybrid system approach. In Proc. of the 45th IEEE conference on decision and control
[11] Van Loan, Charles F., Computing integrals involving the matrix exponential, IEEE Transactions on Automatic Control, AC-23, 3, 395-404 (1978) · Zbl 0387.65013
[12] Van Loan, Charles, The sensitivity of the matrix exponential, SIAM Journal on Numerical Analysis, 14, 6, 971-981 (1977) · Zbl 0368.65006
[13] Walsh, G. C.; Ye, Hong, Scheduling of networked control systems, IEEE Control Systems Magazine, 21, 1, 57-65 (2001)
[14] Wang, Y.; Xie, L.; de Souza, C. E., Robust control of a class of uncertain nonlinear systems, Systems & Control Letters, 19, 2, 139-149 (1992) · Zbl 0765.93015
[15] Yang, T. C., Networked control system: A brief survey, IEE Proceedings on -Control Theory and Applications, 153, 4, 403-412 (2006)
[16] Zhang, Wei; Branicky, M. S.; Phillips, S. M., Stability of networked control systems, IEEE Control Systems Magazine, 21, 1, 84-99 (2001)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.