On positive filtering with ℋ ∞ performance for compartmental networks

This article studies the reduced-order positive filtering problem with ℋ∞ performance of compartmental networks via a system augmentation approach. The filtering system is represented as a system augmentation form, which facilitates the parameterisation with structural constraints. By virtue of system augmentation, a new characterisation of the stability and ℋ∞ performance of the filtering system is established in terms of matrix inequalities. Based on this new characterisation, a necessary and sufficient condition for the existence of a desired filter is proposed, and an iterative algorithm is given to solve the condition. It is emphasised that the significance of the results presented in the article is not any extension of existing approaches or techniques to compartmental networks, but a new framework for filter synthesis. The effectiveness of the theoretical results is shown through some numerical examples.

[1]  Wook Hyun Kwon,et al.  Sufficient LMI conditions for the H∞ output feedback stabilization of linear discrete-time systems , 2004, CDC.

[2]  J. Jacquez.  Compartmental analysis in biology and medicine , 1985 .

[3]  Maysam F. Abbod,et al.  Clinical implementation of advanced control in anaesthesia , 2000 .

[4]  Shengyuan Xu,et al.  Reduced-order H∞ filtering for stochastic systems , 2002, IEEE Trans. Signal Process..

[5]  D. Anderson,et al.  Equilibrium points for nonlinear compartmental models. , 1991, Mathematical biosciences.

[6]  M. C. D. Oliveiraa,et al.  A new discrete-time robust stability condition ( , 1999 .

[7]  S. Rinaldi,et al.  Positive Linear Systems: Theory and Applications , 2000 .

[8]  Irwin W. Sandberg,et al.  On the mathematical foundations of compartmental analysis in biology, medicine, and ecology , 1978 .

[9]  Lihua Xie,et al.  An improved mixed H2/H∞ control design for hard disk drives , 2005, IEEE Trans. Control. Syst. Technol..

[10]  J J DiStefano,et al.  Parameter identifiability and experiment design: thyroid hormone metabolism parameters. , 1977, The American journal of physiology.

[11]  Alessandro Astolfi,et al.  Design of Positive Linear Observers for Positive Linear Systems via Coordinate Transformations and Positive Realizations , 2008, SIAM J. Control. Optim..

[12]  Huijun Gao,et al.  A new design of robust H2 filters for uncertain systems , 2008, Syst. Control. Lett..

[13]  John A. Jacquez,et al.  Qualitative Theory of Compartmental Systems , 1993, SIAM Rev..

[14]  K. Grigoriadis,et al.  Reduced-order H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filtering via linear matrix inequalities , 1997, IEEE Transactions on Aerospace and Electronic Systems.

[15]  Joseph J. DiStefano,et al.  Identification of the dynamics of thyroid hormone metabolism , 1975, Autom..

[16]  A. Astolfi,et al.  Positive linear observers for positive linear systems: a Sylvester equation approach , 2006, 2006 American Control Conference.

[17]  J. Geromel,et al.  Extended H 2 and H norm characterizations and controller parametrizations for discrete-time systems , 2002 .

[18]  J. M. V. den.  Positive Linear Observers for Linear Compartmental Systems , 1998 .

[19]  H. Mounier,et al.  Using token leaky buckets for congestion feedback control in packets switched networks with guaranteed boundedness of buffer queues , 2003, 2003 European Control Conference (ECC).

[20]  Wassim M. Haddad,et al.  Optimal fixed-structure control for linear non-negative dynamical systems , 2004 .

[21]  A. W. Kelman,et al.  Compartmental models and their application , 1985 .

[22]  Y. Ohta,et al.  Asymptotic behavior of nonlinear compartmental systems: Nonoscillation and stability , 1978 .

[23]  Wook Hyun Kwon,et al.  Sufficient LMI conditions for the H/sub /spl infin// output feedback stabilization of linear discrete-time systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[24]  James Lam,et al.  New approach to mixed H/sub 2//H/sub /spl infin// filtering for polytopic discrete-time systems , 2005, IEEE Transactions on Signal Processing.

[25]  D. Fife,et al.  Which linear compartmental systems contain traps , 1972 .

[26]  F. Tadeo,et al.  Positive observation problem for linear discrete positive systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[27]  Truong Q. Nguyen,et al.  Robust and reduced-order filtering: new LMI-based characterizations and methods , 2001, IEEE Trans. Signal Process..

[28]  J J DiStefano,et al.  Comprehensive kinetics of triiodothyronine production, distribution, and metabolism in blood and tissue pools of the rat using optimized blood-sampling protocols. , 1982, Endocrinology.

[29]  E. Sánchez,et al.  OPTIMAL LINEAR FILTERING FOR SYSTEMS WITH MULTIPLE STATE AND OBSERVATION DELAYS , 2007 .

[30]  M. Basin,et al.  OPTIMAL STATE ESTIMATION FOR CONTINUOUS STOCHASTIC STATE-SPACE SYSTEM WITH HYBRID MEASUREMENTS , 2006 .

[31]  G. Bastin,et al.  Positive linear observers for positive linear systems , 1999, 1999 European Control Conference (ECC).