A new shift-invariant representation for periodic linear systems. (English) Zbl 0729.93034

Summary: This paper presents a new family of shift-invariant representations for periodic linear discrete-time systems. This representation has the advantages over the standard representation [R. E. Kalman and J. E. Bertram, J. Franklin Inst. 267, 405-436 (1959; Zbl 0142.070)] of preserving the time step of the original system, and of preserving causality under arbitrary feedback. The disadvantage is that the realization is not minimal. An application in attitude determination is presented.


93C05 Linear systems in control theory
93C55 Discrete-time control/observation systems
93E11 Filtering in stochastic control theory


Zbl 0142.070
Full Text: DOI


[1] Araki, M.; Yamamoto, K., Multivariable multirate sampled-data systems: State-space description, transfer characteristics, and Nyquist criterion, IEEE Trans. Automat. Control, 31, 2, 145-154 (1986)
[2] Farrenkopf, R. L., Analytic steady-state accuracy solutions for two common spacecraft attitude estimators, AIAA J. Guidance and Control, 1, 4, 282-284 (1978)
[3] Flamm, D. S., A new shift-invariant representation for periodic linear systems, (Proc. American Control Conference. Proc. American Control Conference, San Diego, CA (May 1990)), 1510-1515 · Zbl 1354.70035
[4] Francis, B. A.; Georgiou, T. T., Stability theory for linear time-invariant plants with periodic digital controllers, IEEE Trans. Automat. Control, 33, 9, 820-832 (1988) · Zbl 0651.93053
[5] Kalman, R. E.; Bertram, J. E., A unified approach to the theory of sampling systems, J. Franklin Inst., 267, 405-436 (1959) · Zbl 0142.07004
[6] Khargonekar, P. P.; Poolla, K.; Tannenbaum, A., Robust control of linear time-invariant plants using periodic compensation, IEEE Trans. Automat. Control, 30, 11, 1088-1096 (1985) · Zbl 0573.93013
[7] Kranc, G. M., Input-output analysis of multirate feedback systems, IEE Trans. Automat. Control, 3, 21-28 (1957)
[8] Thompson, I. C.; Quasius, G. R., Attitude determination for the P80-1 Satellite, (Proc. Rocky Mountain Guidance and Control Conf.. Proc. Rocky Mountain Guidance and Control Conf., Feb. 1980, Keystone, CO. Proc. Rocky Mountain Guidance and Control Conf.. Proc. Rocky Mountain Guidance and Control Conf., Feb. 1980, Keystone, CO, Advances in the Astronautical Sciences, Vol. 42 (1980), Amer. Astron. Soc), 3-21
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