Strictly passive FIR filtering for state-space models with external disturbance

Abstract This paper proposes a new strictly passive filter with a finite impulse response (FIR) structure for linear state-space signal models with external disturbance. This filter is called a strictly passive FIR filter (SPFF). We apply the strict passivity concept to derive a new linear filter with FIR structure and quasi-deadbeat property. The gain matrix of the proposed SPFF in this paper can be determined by resorting to the solution to a linear matrix inequality (LMI) feasibility problem. An illustrative example is presented to show the validity of the SPFF.

[1]  Wook Hyun Kwon,et al.  A receding horizon Kalman FIR filter for linear continuous-time systems , 1999, IEEE Trans. Autom. Control..

[2]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[3]  Harold Brown,et al.  Integrated Flight and Propulsion Operating Modes for Advanced Fighter Engines , 1983 .

[4]  Alfred M. Bruckstein,et al.  Recursive limited memory filtering and scattering theory , 1985, IEEE Trans. Inf. Theory.

[5]  R. Fitzgerald.  Divergence of the Kalman filter , 1971 .

[6]  Wook Hyun Kwon,et al.  A receding horizon unbiased FIR filter for discrete-time state space models , 2002, Autom..

[7]  S. Sangsuk-Iam,et al.  Analysis of discrete-time Kalman filtering under incorrect noise covariances , 1990 .

[8]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[9]  Wook Hyun Kwon,et al.  $cal H_infty$FIR Filters for Linear Continuous-Time State–Space Systems , 2006, IEEE Signal Processing Letters.

[10]  W. H. Kwon,et al.  FIR filters and recursive forms for continuous time-invariant state-space models , 1987 .

[11]  A. Isidori,et al.  Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems , 1991 .

[12]  Chung Seop Jeong,et al.  An LMI approach to discrete-time observer design with stochastic resilience , 2006 .

[13]  Wook Hyun Kwon,et al.  ${\cal H}_{\infty}$ Finite Memory Controls for Linear Discrete-Time State-Space Models , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[14]  Mohinder S. Grewal,et al.  Kalman Filtering: Theory and Practice , 1993 .

[15]  F. Samarotto.  David Neumeyer and Susan Tepping. A Guide to Schenkerian Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1992 , 1993 .

[16]  Soohee Han,et al.  H 2 , H ∞ , and mixed H 2 /H ∞ FIR Filters for Discrete-time State Space Models , 2003 .