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Stability analysis of digital feedback control systems with time-varying sampling periods. (English) Zbl 0941.93034
The authors study qualitative properties of a class of digital control systems with time-varying sampling periods consisting of a continuous-time nonlinear plant described by systems of first order differential equations, a nonlinear digital controller described by systems of first order difference equations, and appropriate interface elements between the plant and controller (A/D and D/A converters). Using a linearization approach, they establish several sets of conditions for Lyapunov stability and instability of the trivial solution and apply these results to the analysis of certain classes of switched systems and they study a stabilization problem for nonlinear cascaded control systems via hybrid feedback controllers.

93C57 Sampled-data control/observation systems
93B18 Linearizations
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93D15 Stabilization of systems by feedback
Full Text: DOI
[1] Ackerman, J. (1985). Sampled-data control systems: Analysis and synthesis, robust system design. New York: Springer.
[2] Antsaklis, P. J., & Michel, A. N. (1997). Linear systems. New York: McGraw-Hill.
[3] Francis, B.A.; Georgiou, T.T., Stability theory for linear time-invariant plants with periodic digital controllers, IEEE transactions on automatic control, 33, 9, 820-832, (1988) · Zbl 0651.93053
[4] Franklin, G. F., & Powell, J. D. (1980). Digital control of dynamic systems. Reading, MA: Addison-Wesley.
[5] Hou, L.; Michel, A.N.; Ye, H., Some qualitative properties of sampled-data control system, IEEE transactions on automatic control, 42, 12, 1721-1725, (1997) · Zbl 1041.93541
[6] Hu, B.; Michel, A.N., Some qualitative properties of multirate digital control systems, IEEE transactions on automatic control, 44, 4, 765-770, (1999) · Zbl 0958.93062
[7] Hu, B.; Michel, A.N., Stability analysis of a class of multirate digital control systems, Circuits systems and signal processing, 18, 1, 43-57, (1999) · Zbl 0951.93049
[8] Hu, B., & Michel, A. N. (1999c). Robustness analysis of digital feedback control systems with time-varying sampling periods. Proceedings of the 1999 American control conference San, Diego, Caliornia (pp. 3484-3488).
[9] Liberzon, D.; Morse, A.S., Basic problems in stability and design of swiched systems, IEEE control systems magzine, 19, 5, 59-70, (1999) · Zbl 1384.93064
[10] Michel, A. N., & Wang, K. (1995). Qualitative theory of dynamical systems. New York: Marcel Dekker.
[11] Miller, R. K., & Michel, A. N. (1982). Ordinary differential equations. New York: Academic Press. · Zbl 0552.34001
[12] Morse, A. S. (1995). Control using logic-based switching. In A. Isidori (Ed.), Trends in control: A European perspective (pp. 69-113). Berlin: Springer.
[13] Rui, C., Kolmanovsky, I., & McClamroch, N. H. (1997). Hybrid control for stabilization of a class of cascade nonlinear systems. Proceedings of the 1997 American control conference (pp. 2800-2804).
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