On the analysis of periodic linear systems

Tornambè, Antonio

Kybernetika, Tome 32 (1996) no. 6, pp. 625-644

Détail

Classification : 49N20, 93C15

Bibliographie

[1] M. Araki, K. Yamamoto: Multivariable multirate sampled-data systems: state space description, transfer characteristics, and Nyquist criterion. IEEE Trans. Automat. Control AC-31 (1986), 145-154. | MR

[2] S. Bittanti: Deterministic and stochastic linear periodic systems. In: Time Series and Linear Systems (S. Bittanti, ed.), Springer-Verlag, Berlin 1986, pp. 141-182. | MR

[3] S. Bittanti, P. Bolzern: Discrete-time linear periodic systems: gramian and modal criteria for reachability and controllability. Internat. J. Control 41 (1985), 909-928. | MR | Zbl

[4] R. W. Brockett: Finite Dimensional Linear Systems. Wiley, New York 1970. | Zbl

[5] C. T. Chen: Linear System Theory and Design. Holt, Rinehart and Winston, New York 1984.

[6] P. Colaneri: Zero-error regulation of discrete-time linear periodic systems. Systems Control Lett. 15 (1990), 2, 161-167. | MR | Zbl

[7] G. Conte A. M. Perdon, S. Longhi: Invertibility and inversion of linear periodic systems. In: Preprints of the 11th IFAC World Congress, Vol. 2, Tallin 1990, pp. 241-244. | MR

[8] G. Conte A. M. Perdon, S. Longhi: Zero structure at infinity of linear periodic systems. Circuits Systems Signal Process. 10 (1991), 1, 91-100. | MR

[9] D. S. Evans: Finite-dimensional realizations of discrete-time weighting patterns. SIAM J. Appl. Math. 22 (1972), 45-67. | MR | Zbl

[10] M. Fjeld: Optimal control of multivariable periodic processes. Automatica 5 (1969), 497-506. | Zbl

[11] O. M. Grasselli: A canonical decomposition of linear periodic discrete-time systems. Internat. J. Control 40 (1984), 1, 201-214. | MR | Zbl

[12] O. M. Grasselli: Dead-beat observers of reduced order for linear periodic discrete-time systems with inaccessible inputs. Internat. J. Control 40 (1984), 731-745. | Zbl

[13] O. M. Grasselli, F. Lampariello: Dead-beat control of linear periodic discrete-time systems. Internat. J. Control 33 (1981), 1091-1106. | MR | Zbl

[14] O. M. Grasselli, S. Longhi: Disturbance localization with dead-beat control for linear periodic discrete-time systems. Internat. J. Control 44 (1986), 5, 1319-1347. | MR | Zbl

[15] O. M. Grasselli, S. Longhi: Output dead-beat controllers and function dead-beat observers for linear periodic discrete-time systems. Internat. J. Control 43 (1986), 2, 517-537. | MR | Zbl

[16] O. M. Grasselli, S. Longhi: Disturbance localization by measurement feedback for linear periodic discrete-time systems. Automatica 24 (1988), 3, 375-385. | MR | Zbl

[17] O. M. Grasselli, S. Longhi: Pole placement for non-reachable periodic discrete-time systems. Math. Control Signals Systems 4 (1991), 439-455. | MR

[18] O. M. Grasselli, S. Longhi: Robust tracking and regulation of linear periodic discrete-time systems. Internat. J. Control 54 (1991), 3, 613-633. | MR | Zbl

[19] O. M. Grasselli, S. Longhi: Block decoupling with stability of linear periodic systems. J. Math. Systems Estimation Control 3 (1993), 4, 427-458. | MR | Zbl

[20] O. M. Grasselli, S. Longhi: Linear function dead-beat observers with disturbance localization for linear periodic discrete-time systems. Internat. J. Control 45 (1987), 5, 1603-1627. | MR | Zbl

[21] O. M. Grasselli, S. Longhi: Zeros and poles of linear periodic multivariable discrete-time systems. Circuits Systems Signal Process. 7 (1988), 3, 361-380. | MR | Zbl

[22] O. M. Grasselli, S. Longhi: Finite zero structure of linear periodic discrete-time systems. Internat. J. Systems Sci. 22 (1991), 10, 1785-1806. | MR | Zbl

[23] O. M. Grasselli, S. Longhi: The geometric approach for linear periodic discrete-time systems. Linear Algebra Appl. 158 (1991), 27-60. | MR | Zbl

[24] J. Hale: Theory of Functional Differential Equations. Springer-Verlag, New York 1977. | MR | Zbl

[25] M. Kono: Eigenvalue assignment in linear periodic discrete-time systems. Internat. J. Control 32 (1980), 149-158. | MR | Zbl

[26] M. Kono T. Suzuki, T. Morishita: Block decoupling problem of linear $\omega$-periodic discrete-time systems. IEEE Trans. Automat. Control 35 (1990), 1262-1265. | MR

[27] S. Longhi A. M. Perdon, G. Conte: Geometric and algebraic structure at infinity of discrete-time linear periodic systems. Linear Algebra Appl. 122/123/124 (1989), 245-271. | MR

[28] R. A. Meyer, C. S. Burrus: A unified analysis of multirate and periodically time-varying digital filters. IEEE Trans. Circuits and Systems 22 (1975), 162-168. | MR

[29] C. Nikias: A general realization scheme of periodically time-varying digital filters. IEEE Trans. Circuits and Systems 32 (1985), 204-207.

[30] B. Park, E. I. Verriest: Canonical forms on discrete linear periodically time-varying systems and a control application. In: Proc. of the 28th IEEE CDC, Tampa 1989, pp. 1220-1225. | MR

[31] J. A. Richards: Analysis of Periodically Time-varying Systems. Springer-Verlag, Berlin 1983. | Zbl

[32] E. I. Verriest: The operational transfer function and parametrization of N-periodic systems. In: Proc. of the 27th IEEE CDC, Austin 1988, 1994-1999.

[33] J. Vlach K. Singhal, M. Vlach: Computer oriented formulation of equations and analysis of switched-capacitor networks. IEEE Trans. Circuits and Systems 31 (1984), 753-765.

[34] L. Zheng: Discrete-time adaptive control for periodically time-varying systems. In: Proc. of the IFAC Symp. on Adaptive Systems in Control and Signal Processing, Lund 1986, pp. 131-135.