Non-pathological sampling for generalized sampled-data hold functions. (English) Zbl 0821.93057
Summary: Given a generalized sampled-data hold function (GSHF), we define a frequency dependent response function having many properties analogous to those of a transfer function. In particular, the zeros of the response function have transmission blocking properties. We then study the problem of non-pathological sampling with a GSHF. Sampling is said to be pathological if the discretized version of a stabilizable/detectable continuous time plant is not itself stabilizable and detectable. Sufficient conditions for non-pathological sampling with a zero order hold have long been known. We extend these to the case of a GSHF, and describe the role in non-pathological sampling played by right half plane zeros of the response function. The results are presented for square multivariable linear systems and include a generalization to allow for a time delay.
MSC:
| 93C57 | Sampled-data control/observation systems |
| 34K35 | Control problems for functional-differential equations |
| 93B05 | Controllability |
| 93B07 | Observability |
Keywords:
generalized sampled-data hold function; response function; zeros; stabilizable; detectable; linear; time delayReferences:
| [1] | Araki, M., Recent developments in digital control theory, (Proc. 12th IFAC World Congress, Sydney, Australia, (1993)) |
| [2] | Åström, K. J.; Wittenmark, B., (Computer-controlled Systems, Theory and Design, (1990), Prentice-Hall Englewood Cliffs, New Jersey) · Zbl 0217.57903 |
| [3] | Francis, B. A.; Georgiou, T. T., Stability theory for liner time-invariant plants with periodic digital controllers, IEEE Trans. Autom. Contr., 820-832, (1988) · Zbl 0651.93053 |
| [4] | Kabamba, P. T., Control of linear systems using generalised sampled-data hold functions, EEE Trans. Autom. Contr., 772-783, (1987) · Zbl 0627.93049 |
| [5] | Kailath, T., (Linear Systems, (1980), Prentice-Hall Englewood Cliffs, New Jersey) · Zbl 0458.93025 |
| [6] | Kalman, R.; Ho, B. L.; Narendra, K., Controllability of linear dynamical systems, (Contributions to Differential Equations, Vol. 1, (1963), Interscience New York) · Zbl 0151.13303 |
| [7] | Middleton, R. H.; Freudenberg, J., Zeros and non-pathological sampling for generalised sampled-data hold functions, (Technical Report EE9318, (1993), Department of Electrical and Computer Engineering, University of Newcastle Australia), 2308 |
| [8] | Ortega, R.; Kreisselmeier, G., Discrete-time model reference adaptive control for continuous-time systems using generalised sampled-data hold functions, IEEE Trans. Autom. Contr., 334-338, (1990) · Zbl 0707.93034 |
| [9] | Yan, W.; Anderson, B. D.O.; Bitmead, R. R., On the gain margin improvement using dynamic compensation based on generalized sampled-data hold functions, (Technical Report, (1989), Department of Systems Engineering, Australian National University) · Zbl 0825.93435 |
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