Output regulation, tracking and nominal decoupling with stability for uncertain linear periodic systems

In this paper uncertain linear periodic discrete-time systems are considered, for obtaining the row-by-row reference-output decoupling with stability at the nominal parameters, together with the asymptotic tracking and output regulation in a neighbourhood of the nominal parameters, for classes of exponential-polynomial reference signals and exponential disturbance functions. By-using the periodic version of the internal model principle, the necessary and sufficient conditions for the existence of a solution are given, and a design procedure for the dynamic compensator is proposed.

[1]  S. Bittanti.  Deterministic and stochastic linear periodic systems , 1986 .

[2]  David S. Evans,et al.  FINITE-DIMENSIONAL REALIZATIONS OF DISCRETE-TIME WEIGHTING PATTERNS* , 1972 .

[3]  O. Grasselli,et al.  Finite zero structure of linear periodic discrete-time systems , 1991 .

[4]  Erik I. Verriest,et al.  Canonical forms on discrete linear periodically time-varying systems and a control application , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[5]  Erik I. Verriest,et al.  Periodic Systems Realization Theory with applications , 1994 .

[6]  J. Dion,et al.  The minimal delay decoupling problem: feedback implementation with stability , 1988 .

[7]  Patrizio Colaneri,et al.  The realization problem for linear periodic systems , 1995, Autom..

[8]  P. Valigi,et al.  Decoupling with stability for linear periodic systems , 1996 .

[9]  J. Descusse.  State feedback decoupling with stability of linear constant ( A,B,C,D ) quadruples , 1980 .

[10]  P. Falb,et al.  Decoupling in the design and synthesis of multivariable control systems , 1967, IEEE Transactions on Automatic Control.

[11]  David S. Flamm,et al.  A new shift-invariant representation for periodic linear systems , 1991 .

[12]  D. S. Flamm.  Single-loop stability margins for multirate and periodic control systems , 1993, IEEE Trans. Autom. Control..

[13]  C. Sidney Burrus,et al.  A unified analysis of multirate and periodically time-varying digital filters , 1975 .

[14]  Antonio Tornambè,et al.  Robust ripple-free regulation and tracking for parameter-dependent sampled-data systems , 1996, IEEE Trans. Autom. Control..

[15]  Bruce A. Francis,et al.  The internal model principle of control theory , 1976, Autom..

[16]  Antonio Tornambè,et al.  System Equivalence for Periodic Models and Systems , 1995 .

[17]  Patrizio Colaneri,et al.  Zero-error regulation of discrete-time linear periodic systems , 1990 .

[18]  Antonio Tornambè,et al.  Robust output regulation and tracking for linear periodic systems under structured uncertainties , 1996, Autom..

[19]  A. Morse,et al.  Decoupling and Pole Assignment in Linear Multivariable Systems: A Geometric Approach , 1970 .

[20]  B. Francis.  The linear multivariable regulator problem , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[21]  Marco Lovera,et al.  On the Zero Dynamics of Helicopter Rotor Loads , 1996, Eur. J. Control.

[22]  O. Grasselli,et al.  Robust tracking and regulation of linear periodic discrete-time systems , 1991 .

[23]  O. Grasselli,et al.  Pole placement for nonreachable periodic discrete-time systems , 1991 .

[24]  Antonio Tornambè,et al.  Robust tracking and performance for multivariable systems under physical parameter uncertainties, , 1993, Autom..

[25]  Ching-An Lin,et al.  Minimal Periodic Realizations of Transfer Matrices , 1992, 1992 American Control Conference.

[26]  Thomas Kailath,et al.  Linear Systems , 1980 .

[27]  Sauro Longhi,et al.  Robust output regulation under uncertainties of physical parameters , 1991 .

[28]  E. Davison.  The robust control of a servomechanism problem for linear time-invariant multivariable systems , 1976 .

[29]  A. Tornambe,et al.  Robust tracking and disturbance rejection under physical parameter uncertainties for polynomial-exponential signals , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[30]  M. Heymann,et al.  Linear feedback decoupling--Transfer function analysis , 1983 .