Finite-Time Stability and Control of 2D Continuous–Discrete Systems in Roesser Model
This study is conducted to investigate stability and control problems within a finite-time interval for a 2D continuous–discrete system in Roesser model. The concepts of finite-time stability (FTS) and finite-time boundedness (FTB) are naturally extended to the 2D continuous–discrete system. Recursive relations between system states are first obtained, then sufficient conditions for FTS and FTB in the system are derived, and a finite-time controller is supplied to the system. Sufficient conditions for finite-time stabilization are also provided for the linear repetitive process. Examples of metal rolling operation are presented to illustrate the proposed method.
Keywords2D continuous–discrete system Finite-time stability Finite-time boundedness Linear repetitive process
The authors would like to thank the National Natural Science Foundation of China under Grant 61573007 and Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20133219110040 for financial support.
- 5.M. Buslowicz, Stability and robust stability conditions for a general model of scalar continuous–discrete linear systems. Pomiary, Automatyka, Kontrola 56, 133–135 (2010)Google Scholar
- 10.P. Dorato, C. Abdallah, D. Famularo, Robust finite-time stability design via linear matrix inequalities, in IEEE Conference on Decision and Control. Institute of Electrical Engineers INC (IEE). (1997)Google Scholar
- 11.K. Galkowski, J. Wood, Multidimensional Signals, Circuits and Systems, Systems and Control Book Series (Taylor and Francis, London, England, 2001)Google Scholar
- 18.S. Knorn, A two-dimensional systems stability analysis of vehicle platoons (National University, Maynooth, 2013)Google Scholar
- 20.A. Lebedev, The problem of stability in a finite interval of time. J. Appl. Math. Mech. (PMM) 18, 75–94 (1954)Google Scholar
- 21.Y. Li, M. Cantoni, E. Weyer, On water-level error propagation in controlled irrigation channels, in Proceedings of IEEE Conference on Decision Control and European Control Conference, (Seville, Spain, 2005), pp. 2101–2106Google Scholar
- 26.W. Paszke, O. Bachelier, New robust stability and stabilization conditions for linear repetitive processes, in International Workshop on Multidimensional, (IEEE, 2009), pp. 1–6 Google Scholar
- 27.W. Paszke, P. Dabkowski, E. Rogers, K. Galkowski, Stability and robustness of discrete linear repetitive processes in the finite frequency domain using the KYP lemma, in IEEE 52nd Annual Conference on Decision and Control (CDC), 2013, pp. 3421–3426 (2013)Google Scholar
- 38.W. Zhang, X. An, Finite-time control of linear stochastic systems. Int. J. Innov. Comput. Inf. Control 4(3), 689–696 (2008)Google Scholar