Induced l∞ stability of fixed-point digital filters without overflow oscillations and instability due to finite word length effects

This article studies a new criterion for the induced l∞ stability of fixed-point state-space digital filters without overflow oscillations and instability due to finite word length effects. The criterion not only guarantees exponential stability but also reduces the effect of external interference to an induced l∞ norm constraint. We present a numerical example, which demonstrates the effectiveness of the proposed criterion.

[1]  Vimal Singh.  LMI Approach to Stability of Direct Form Digital Filters Utilizing Single Saturation Overflow Nonlinearity , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[3]  C. Ahn.  Criterion for the elimination of overflow oscillations in fixed-point digital filters with saturation arithmetic and external disturbance , 2011 .

[4]  Irwin W. Sandberg.  The zero-input response of digital filters using saturation arithmetic , 1979 .

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

[6]  Gilbert Strang,et al.  Introduction to applied mathematics , 1988 .

[7]  Vimal Singh,et al.  A new criterion for the overflow stability of second-order state-space digital filters using saturation arithmetic , 1998 .

[8]  Vimal Singh.  Stability analysis of a class of digital filters utilizing single saturation nonlinearity , 2008, Autom..

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

[10]  Vimal Singh,et al.  Stability analysis of discrete-time systems in a state-space realisation with partial state saturation nonlinearities , 2003 .

[11]  Hannu Tenhunen,et al.  Switching Sensitive Driver Circuit to Combat Dynamic Delay in On-Chip Buses , 2005, PATMOS.

[12]  Yannis Tsividis,et al.  Mixed analog-digital VLSI devices and technology , 1996 .

[13]  Michael G. Taylor,et al.  Overflow oscillations in digital filters , 1969 .

[14]  Vimal Singh.  Elimination of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic , 1990 .

[15]  L. Ghaoui,et al.  History of linear matrix inequalities in control theory , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[16]  Vassilis Paliouras,et al.  Integrated Circuit and System Design. Power and Timing Modeling, Optimization and Simulation , 2005, Lecture Notes in Computer Science.

[18]  Haranath Kar,et al.  Elimination of overflow oscillations in digital filters employing saturation arithmetic , 2005, Digit. Signal Process..

[19]  Wolfgang Nebel,et al.  Integrated Circuit and System Design. Power and Timing Modeling, Optimization and Simulation , 2012, Lecture Notes in Computer Science.

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