Title :
On MMSE, mutual information and Popov function in continuous-time multivariable linear systems
Author_Institution :
Dept. of Control Sci. & Eng., Zhejiang Univ., Hangzhou, China
Abstract :
By analyzing information transmission in stable and unstable, open- and closed-loop linear continuous-time Gaussian systems, connections within the MMSE of causal estimation, mutual information rate, and the integral of a Popov function are discussed. Yovits´ equality for scalar stable systems and Anderson´s equality for scalar unstable systems concerning MMSE are extended to multivariable systems. As a consequent result, it is concluded that the mutual information rate between system state and output is changed by feedback, and the variation of time-average information transmission is defined by a Bode- like integral function which is related to the causal filtering MMSE and the Popov integral function under a special feedback gain.
Keywords :
Gaussian processes; Popov criterion; closed loop systems; continuous time systems; feedback; integral equations; least mean squares methods; linear systems; multivariable systems; open loop systems; Anderson´s equality; Bode-like integral function; Popov integral function; Yovits´ equality; causal estimation; causal filtering MMSE; closed-loop linear continuous-time Gaussian systems; continuous-time multivariable linear systems; feedback gain; information transmission; mutual information; mutual information rate; open-loop linear continuous-time Gaussian systems; scalar stable systems; stable linear continuous-time Gaussian systems; system state; time-average information transmission; unstable linear continuous-time Gaussian systems; Closed loop systems; Covariance matrix; Estimation; Filtering; Mutual information; Signal to noise ratio; Transfer functions;
Conference_Titel :
Control Applications (CCA), 2012 IEEE International Conference on
Conference_Location :
Dubrovnik
Print_ISBN :
978-1-4673-4503-3
Electronic_ISBN :
1085-1992
DOI :
10.1109/CCA.2012.6402458
