Information theoretic limit and bound of disturbance rejection in LTI systems: Shannon entropy and H/sub /spl infin// entropy

By investigating the transmission of information and uncertainty in multivariable LTI systems disturbed by stationary random processes, the present paper discussed the connections within information rates, Bode integral and H/sub /spl infin// entropy. For the regulation problem, performance limits of disturbance rejection are formulated in the framework of information theory, by connecting entropy rate to Bode integral formula. The "conservation law of variety" is revised. For the tracking problem, an upper bound of disturbance rejection performance is derived based on a proved relation between information rates and H/sub /spl infin// entropy. The present results demonstrate that information rates are useful in control system analysis.

[1]  Amiel Feinstein,et al.  Information and information stability of random variables and processes , 1964 .

[2]  Shunsuke Ihara,et al.  Information theory - for continuous systems , 1993 .

[3]  Hong Wang,et al.  Minimum entropy control of non-Gaussian dynamic stochastic systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[4]  M. Rosenblatt.  Asymptotic distribution of eigenvalues of block Toeplitz matrices , 1960 .

[5]  Pablo A. Iglesias,et al.  Discrete time H ∞ controllers satisfying a minimum entropy criterion , 1990 .

[6]  Sebastian Engell.  VARIETY, INFORMATION AND FEEDBACK , 1984 .

[7]  Jie Chen.  Sensitivity integrals and transformation techniques: a new perspective , 1997, IEEE Trans. Autom. Control..

[8]  Pablo A. Iglesias,et al.  Tradeoffs in linear time-varying systems: an analogue of Bode's sensitivity integral , 2001, Autom..

[9]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[10]  H. W. Bode,et al.  Network analysis and feedback amplifier design , 1945 .

[11]  Tongwen Chen,et al.  Multirate sampled-data systems: all H∞ suboptimal controllers and the minimum entropy controller , 1999, IEEE Trans. Autom. Control..

[12]  J. Ackermann,et al.  Robust control , 2002 .

[13]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[14]  Hui Zhang,et al.  Bode integrals and laws of variety in linear control systems , 2003, Proceedings of the 2003 American Control Conference, 2003..

[15]  Graham C. Goodwin,et al.  Fundamental Limitations in Filtering and Control , 1997 .

[16]  J. H. van Schuppen,et al.  System identification with information theoretic criteria , 1995 .