Stabilization of multirate sampled-data linear systems. (English) Zbl 0712.93046

Summary: This paper considers the design of multiple-input multiple-output digital control systems characterized by a non-standard sampling mechanism. It is assumed that the various outputs of the plant are measured at different rates, which can be definitively less than the unique rate adopted for the inputs updating, or else at different times. A pole-placement problem is solved by resorting to a controller composed by a periodic state observer and a non-dynamic control law.


93D15 Stabilization of systems by feedback
93B55 Pole and zero placement problems
93C05 Linear systems in control theory
93C55 Discrete-time control/observation systems
93C35 Multivariable systems, multidimensional control systems
93C57 Sampled-data control/observation systems
Full Text: DOI


[1] Amit, N.; Powell, J. D., Optimal digital control of multirate systems, (Proc. AIAA Guidance and Control Conf.. Proc. AIAA Guidance and Control Conf., Albuquerque (1981)), 423-429
[2] Araki, M.; Hagiwara, T., Pole assignment by multirate sampled-data output feedback, Int. J. Control, 44, 1661-1673 (1986) · Zbl 0613.93040
[3] Araki, M.; Yamamoto, K., Multivariable multirate sampled-data systems: state-space description, transfer characteristics, and Nyquist criterion, IEEE Trans. Aut. Control, AC-31, 145-154 (1986)
[4] Bittanti, S., Deterministic and stochastic linear periodic systems, (Time Series and Linear Systems (1986), Springer-Verlag), 141-182
[5] Bittanti, S.; Colaneri, P.; De Nicolao, G., The difference periodic Riccati equation for the periodic prediction problem, IEEE Trans. Aut. Control, AC-33, 706-712 (1988) · Zbl 0656.93067
[6] Bolzern, P.; Colaneri, P., Inertia theorems for the periodic Lyapunov difference equation and periodic Riccati difference equation, Linear Algebra and its Applications, 85, 249-265 (1987) · Zbl 0614.39002
[7] Chammas, A. B.; Leondes, C., Pole assignment by piecewise constant output feedback, Int. J. Control, 29, 31-38 (1979) · Zbl 0443.93042
[8] Colaneri, P.; Scattolini, R.; Schiavoni, N., A design technique for multirate control with application to a distillation column, (Proc. 12th IMACS World Congr., Vol. 2 (1988)), 589-591
[9] Francis, B. A.; Georgiou, T. T., Stability theory for linear time-invariant plants with periodic digital controllers, IEEE Trans. Aut. Control, AC-33, 820-832 (1988) · Zbl 0651.93053
[10] Jury, E. I., A note on multirate sampled-data systems, IEEE Trans. Aut. Control, AC-12, 319-320 (1967)
[11] Kabamba, P. T., Monodromy eigenvalue assignment in linear periodic systems, IEEE Trans. Aut. Control, AC-31, 950-952 (1986) · Zbl 0596.93022
[12] Kabamba, P. T., Control of linear systems using generalized sampled-data hold functions, IEEE Trans. Aut. Control, AC-32, 772-783 (1987) · Zbl 0627.93049
[13] Kailath, T., (Linear Systems (1980), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ) · Zbl 0458.93025
[14] 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
[15] Khargonekar, P. P.; Poola, K.; Tannenbaum, A., Robust control of linear time-invariant plants using periodic compensation, IEEE Trans. Aut. Control, AC-30, 1088-1096 (1985) · Zbl 0573.93013
[16] Kranc, G. M., Input-output analysis of multirate feedback system, IRE Trans. Aut. Control, 3, 21-28 (1957)
[17] Meyer, R. A.; Burrus, C. S., A unified analysis of multirate and periodically time-varying digital filters, IEEE Trans. Ccts Syst., CAS-22, 162-168 (1975)
[18] Scattolini, R., Self-tuning control of systems with infrequent and delayed output sampling, (Proc. IEE-D, 135 (1988)), 213-221 · Zbl 0665.93039
[19] Scattolini, R.; Schiavoni, N., Design of multirate control systems via parameter optimization, 26th IEEE CDC, Vol. 2, 1556-1557 (1987)
[20] Söderström, T.; Lennartson, B., On linear optimal control with infrequent output sampling, (Proc. 3rd IMA Conf. on Control Theory (1981), Academic Press: Academic Press New York), 605-624
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.