Disturbance Localization with Dead-beat Control by Measurement Feedback for Linear Periodic Discrete-time Systems

Abstract The new notions of inner controllable, outer controllable and outer reconstructible subspace, together with the extensions of the classical notions of controlled invariant and conditioned invariant subspaces to the class of linear periodic discrete-time systems, are the main tools used in this paper in order to study the disturbance localization problem by measurement feedback for the same class of systems. By means of these concepts the necessary and sufficient solvability conditions of such a problem and synthesis procedures of the solutions are found for three different cases, i.e. with and without an additional requirement of output or state dead-beat control.

[1]  Sauro Longhi,et al.  Linear function dead-beat observers for linear periodic discrete-time systems with unknown disturbances , 1986, 1986 25th IEEE Conference on Decision and Control.

[2]  O. M. Grasselli,et al.  Linear function dead-beat observers with disturbance localization for linear periodic discrete-time systems , 1987 .

[3]  O. M. Grasselli,et al.  Dead-beat control of linear periodic discrete-time systems† , 1981 .

[4]  H. Imai,et al.  Disturbance localization and pole shifting by dynamic compensation , 1981 .

[5]  Sauro Longhi,et al.  Disturbance localization with dead-beat control for linear periodic discrete-time systems , 1986 .

[6]  O. M. Grasselli,et al.  On the stabilization of a class of bilinear systems , 1983 .

[7]  G. Hewer.  Periodicity, Detectability and the Matrix Riccati Equation , 1975 .

[8]  J. Schumacher.  Compensator synthesis using (C,A,B)-pairs , 1980 .

[9]  O. M. Grasselli,et al.  Dead-beat observers of reduced order for linear periodic discrete-time systems with inaccessible inputs , 1984 .

[10]  D. Corrall.  On the stability of periodically time varying systems , 1979 .

[11]  Jon H. Davis.  Stability Conditions Derived from Spectral Theory: Discrete Systems with Periodic Feedback , 1972 .

[12]  O. M. Grasselli,et al.  Dead-beat control of discrete-time bilinear systems † , 1980 .

[13]  O. M. Grasselli,et al.  A canonical decomposition of linear periodic discrete-time systems , 1984 .

[14]  S. Bittanti,et al.  H-CONTROLLABILITY AND OBSERVABILITY OF LINEAR PERIODIC SYSTEMS* , 1984 .

[15]  H. E. Meadows,et al.  Solution of systems of linear ordinary differential equations with periodic coefficients , 1962 .

[16]  P. Brunovský.  Controllability and linear closed-loop controls in linear periodic systems , 1969 .

[17]  J. M. Schumacher.  Regulator synthesis using (C,A,B)-pairs , 1982 .

[18]  A. Isidori,et al.  Output regulation of a class of bilinear systems under constant disturbances , 1979, Autom..

[19]  S. Bittanti,et al.  Periodic solutions of periodic Riccati equations , 1984 .

[20]  C. Maffezzoni,et al.  Periodic Systems: Controllability and the Matrix Riccati Equation , 1978 .

[21]  S. Longhi,et al.  Output dead-beat controllers and function dead-beat observers for linear periodic discrete-time systems† , 1986 .

[22]  Hajime Akashi,et al.  Disturbance localization and output deadbeat control through an observer in discrete-time linear multivariable systems , 1979 .

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

[24]  M. Kono.  Eigenvalue assignment in linear periodic discrete-time systems† , 1980 .

[25]  J. Willems,et al.  Disturbance Decoupling by Measurement Feedback with Stability or Pole Placement , 1981 .