Achievable sensitivity bounds for MIMO control systems via an information theoretic approach

Abstract This paper deals with an MIMO feedback control system that has two channels with additive noises and studies the effects of the noises on the input and output signals of the plant. We derive achievable bounds of integral type for sensitivity-like properties of the system based on an information theoretic approach. These bounds are generalizations of Bode’s integral formula for the case that the feedback system includes nonlinear elements.

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

[2]  W. Rudin.  Real and complex analysis , 1968 .

[3]  Munther A. Dahleh,et al.  Fundamental Limitations of Disturbance Attenuation in the Presence of Side Information , 2005, IEEE Transactions on Automatic Control.

[4]  Robin J. Evans,et al.  Stabilizability of Stochastic Linear Systems with Finite Feedback Data Rates , 2004, SIAM J. Control. Optim..

[5]  Panos J. Antsaklis,et al.  Special Issue on Technology of Networked Control Systems , 2007 .

[6]  Shinji Hara,et al.  Properties of sensitivity and complementary sensitivity functions in single-input single-output digital control systems , 1988 .

[7]  Pedro M. Crespo,et al.  Asymptotically Equivalent Sequences of Matrices and Hermitian Block Toeplitz Matrices With Continuous Symbols: Applications to MIMO Systems , 2008, IEEE Transactions on Information Theory.

[8]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[9]  Shinji Hara,et al.  Characterization of a complementary sensitivity property in feedback control: An information theoretic approach , 2009, Autom..

[10]  Shinji Hara,et al.  Properties of complementary sensitivity function in SISO digital control systems , 1989 .

[11]  J. Freudenberg,et al.  Frequency Domain Properties of Scalar and Multivariable Feedback Systems , 1988 .

[12]  Sekhar Tatikonda,et al.  Control over noisy channels , 2004, IEEE Transactions on Automatic Control.

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

[14]  Shinji Hara,et al.  Sensitivity analysis of networked control systems via an information theoretic approach , 2008, 2008 47th IEEE Conference on Decision and Control.

[15]  Sekhar Tatikonda,et al.  Control under communication constraints , 2004, IEEE Transactions on Automatic Control.

[16]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .