A tradeoff between period and order of linear periodic stabilizing compensators

Here we consider the problem of stabilizing a discrete-time linear time-invariant plant by a linear periodic compensator. We show that we can trade off compensator order for an increased period. In particular, with n the plant order, it is shown that for every lϵ {1,…n}, we can do almost arbitrary pole placement using an lth-order, (n + 2 − l)th period, linear periodic controller; for most plants the period can be reduced by one. We also show that first-order linear periodic controllers can be used to solve the strong and simultaneous stabilization problems.

[1]  Bruce A. Francis,et al.  Uniformly optimal control of linear feedback systems , 1985, Autom..

[2]  J. Shamma,et al.  Time-varying versus time-invariant compensation for rejection of persistent bounded disturbances and robust stabilization , 1991 .

[3]  H. Kimura.  Pole assignment by gain output feedback , 1975 .

[4]  L. Fletcher.  An intermediate algorithm for pole placement by output feedback in linear multivariable control systems , 1980 .

[5]  C. Mullis,et al.  On the controllability of discrete linear systems with output feedback , 1973 .

[6]  Bonaventure Intercontinental,et al.  ON DECISION AND CONTROL , 1985 .

[7]  M. Vidyasagar,et al.  Algebraic design techniques for reliable stabilization , 1982 .

[8]  Tadeusz Kaczorek,et al.  Pole placement for linear discrete-time systems by periodic output feedbacks , 1985 .

[9]  D. Meyer.  Two properties of l/sub 1/-optimal controllers , 1988 .

[10]  K. Poolla,et al.  Robust control of linear time-invariant plants using periodic compensation , 1985 .

[11]  H. Kimura.  A further result on the problem of pole assignment by output feedback , 1977 .

[12]  S. Wang,et al.  On pole assignment in linear multivariable systems using output feedback , 1975 .

[13]  D. Youla,et al.  Single-loop feedback-stabilization of linear multivariable dynamical plants , 1974, Autom..

[14]  Daniel E. Miller.  Adaptive stabilization using a nonlinear time-varying controller , 1994, IEEE Trans. Autom. Control..

[15]  Dirk Aeyels,et al.  Pole assignment for linear time-invariant systems by periodic memoryless output feedback , 1992, Autom..

[16]  W. Wonham.  Linear Multivariable Control: A Geometric Approach , 1974 .

[17]  E. Davison,et al.  Properties of linear time-invariant multivariable systems subject to arbitrary output and state feedback , 1973 .

[18]  Hidenori Kimura,et al.  Pole assignment by output feedback: a longstanding open problem , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.