A new solution to the induced l∞ finite impulse response filtering problem based on two matrix inequalities

In this paper, we use an induced l∞ approach to create a new filter with a finite impulse response (FIR) structure for state-space models with external disturbances. This filter is called an induced l∞ FIR filter (ILIFF). The proposed ILIFF’s gain matrix can be determined by solving a linear matrix inequality problem for a fixed positive scalar variable. An illustrative example is given to demonstrate the effectiveness of the ILIFF.

[1]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[2]  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.

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

[4]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[5]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[6]  T. Kailath,et al.  Indefinite-quadratic estimation and control: a unified approach to H 2 and H ∞ theories , 1999 .

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

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

[9]  Arkadi Nemirovski,et al.  Lmi Control Toolbox For Use With Matlab , 2014 .

[10]  Peter Willett,et al.  A Low-Complexity Sliding-Window Kalman FIR Smoother for Discrete-Time Models , 2010, IEEE Signal Processing Letters.

[11]  N. F. Toda,et al.  Divergence in the Kalman Filter , 1967 .

[12]  Choon Ki Ahn.  Input-to-state stable nonlinear filtering for a class of continuous-time delayed nonlinear systems , 2013, Int. J. Control.

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

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

[15]  Alan J. Laub,et al.  The LMI control toolbox , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[16]  K. Poolla,et al.  A linear matrix inequality approach to peak‐to‐peak gain minimization , 1996 .

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

[18]  Yuriy S. Shmaliy,et al.  Unbiased FIR Filtering of Discrete-Time Polynomial State-Space Models , 2009, IEEE Transactions on Signal Processing.

[19]  Choon Ki Ahn,et al.  Strictly passive FIR filtering for state-space models with external disturbance , 2012 .

[20]  Choon Ki Ahn,et al.  Induced l∞ stability of fixed-point digital filters without overflow oscillations and instability due to finite word length effects , 2012 .

[21]  Mathukumalli Vidyasagar,et al.  Optimal rejection of persistent bounded disturbances , 1986 .

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

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

[24]  Choon Ki Ahn,et al.  Robustness bound for receding horizon finite memory control: Lyapunov–Krasovskii approach , 2012, Int. J. Control.

[25]  Yuriy S. Shmaliy,et al.  Linear Optimal FIR Estimation of Discrete Time-Invariant State-Space Models , 2010, IEEE Transactions on Signal Processing.

[26]  Choon Ki Ahn,et al.  Peak-to-peak exponential direct learning of continuous-time recurrent neural network models: a matrix inequality approach , 2013, Journal of Inequalities and Applications.