An improved criterion for the global asymptotic stability of fixed-point state-space digital filters with combinations of quantization and overflow

This paper deals with the problem of global asymptotic stability of fixed-point state-space digital filters under various combinations of quantization and overflow nonlinearities and for the situation where quantization occurs after summation only. Utilizing the structural properties of the nonlinearities in greater detail, a new global asymptotic stability criterion is proposed. A unique feature of the presented approach is that it exploits the information about the maximum normalized quantization error of the quantizer and the maximum representable number for a given wordlength. The approach leads to an enhanced stability region in the parameter-space, as compared to several previously reported criteria.

[1]  Peter H. Bauer,et al.  New criteria for asymptotic stability of one- and multidimensional state-space digital filters in fixed-point arithmetic , 1994, IEEE Trans. Signal Process..

[2]  Tamal Bose.  Combined Effects of Overflow and Quantization in Fixed-Point Digital Filters , 1994 .

[3]  Gian Antonio Mian,et al.  A contribution to the stability analysis of second-order direct-form digital filters with magnitude truncation , 1987, IEEE Trans. Acoust. Speech Signal Process..

[4]  V. Singh,et al.  Stability analysis of 1-D and 2-D fixed-point state-space digital filters using any combination of overflow and quantization nonlinearities , 2001, IEEE Trans. Signal Process..

[5]  Tatsushi Ooba.  Stability of Discrete-Time Systems Joined With a Saturation Operator on the State-Space $ $ , 2010, IEEE Transactions on Automatic Control.

[6]  Haranath Kar.  Asymptotic stability of fixed-point state-space digital filters with combinations of quantization and overflow nonlinearities , 2011, Signal Process..

[7]  T. Claasen,et al.  Effects of quantization and overflow in recursive digital filters , 1976 .

[8]  Bruce W. Bomar.  Low-roundoff-noise limit-cycle-free implementation of recursive transfer functions on a fixed-point digital signal processor , 1994, IEEE Trans. Ind. Electron..

[9]  Tamal Bose,et al.  Stability of digital filters implemented with two's complement truncation quantization , 1992, IEEE Trans. Signal Process..

[10]  Hj Hans Butterweck,et al.  Finite wordlength effects in digital filters : a review , 1988 .

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

[12]  Yuichi Sawada,et al.  KALMAN FILTER BASED LEQG CONTROL OF A PARALLEL- STRUCTURED SINGLE-LINK FLEXIBLE ARM MOUNTED ON MOVING BASE , 2010 .

[13]  B. W. Bomar.  On the design of second-order state-space digital filter sections , 1989 .

[14]  Vimal Singh.  A new realizability condition for limit cycle-free state-space digital filters employing saturation arithmetic , 1985 .

[15]  P. Bauer,et al.  Bounded-input-bounded-output properties of nonlinear discrete difference equations-applications to fixed-point digital filters , 1992 .

[16]  J.H.F. Ritzerfeld.  A condition for the overflow stability of second-order digital filters that is satisfied by all scaled state-space structures using saturation , 1989 .

[17]  A. Michel,et al.  Stability analysis of fixed- point digital filters using computer generated Lyapunov functions- Part I: Direct form and coupled form filters , 1985 .

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

[19]  Adam Kozma,et al.  Comments on "Limit Cycles Due to Roundoff in State-Space Digital Filters" , 1991 .

[20]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[21]  Priyanka Kokil,et al.  An improved criterion for the global asymptotic stability of fixed-point state-space digital filters with saturation arithmetic , 2012, Digit. Signal Process..

[22]  Mário Sarcinelli Filho,et al.  Low-noise zero-input, overflow, and constant-input limit cycle-free implementation of state space digital filters , 2007, Digit. Signal Process..

[23]  B. Bomar.  Computationally efficient low roundoff noise second-order state-space structures , 1986 .

[24]  T. Bose,et al.  Limit cycles in zero input digital filters due to two's complement quantization , 1990 .

[25]  Tao Shen,et al.  An improved stability criterion for fixed-point state-space digital filters using two's complement arithmetic , 2012, Autom..

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

[27]  Haranath Kar.  An LMI based criterion for the nonexistence of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic , 2007, Digit. Signal Process..

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

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

[30]  W. Mecklenbrauker,et al.  Second-order digital filter with only one magnitude-truncation quantiser and having practically no limit cycles , 1973 .

[31]  Haranath Kar.  An improved version of modified Liu-Michel's criterion for global asymptotic stability of fixed-point state-space digital filters using saturation arithmetic , 2010, Digit. Signal Process..

[32]  Vimal Singh,et al.  Elimination of overflow oscillations in fixed-point state-space digital filters with saturation arithmetic: an LMI approach , 2004, IEEE Trans. Circuits Syst. II Express Briefs.

[33]  Vimal Singh.  Modified Form of Liu-Michel's Criterion for Global Asymptotic Stability of Fixed-Point State-Space Digital Filters Using Saturation Arithmetic , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[34]  R. Roberts,et al.  Digital filter realizations without overflow oscillations , 1978 .

[35]  Jingyu Hua,et al.  A novel digital filter structure with minimum roundoff noise , 2010, Digit. Signal Process..

[36]  Jean H. F. Ritzerfeld.  Noise gain expressions for low noise second-order digital filter structures , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[37]  Peter Bauer,et al.  Comments on 'Limit cycles due to roundoff in state-space digital filters' [and reply] , 1991, IEEE Trans. Signal Process..

[38]  I. W. Sandberg,et al.  A separation theorem for finite precision digital filters , 1995 .

[39]  Peter H. Bauer,et al.  Stability analysis of multidimensional (m-D) direct realization digital filters under the influence of nonlinearities , 1988, IEEE Trans. Acoust. Speech Signal Process..

[40]  A. Michel,et al.  Asymptotic stability of discrete-time systems with saturation nonlinearities with applications to digital filters , 1992 .

[41]  David P. Brown,et al.  Limit cycles due to roundoff in state-space digital filters , 1990, IEEE Trans. Acoust. Speech Signal Process..

[42]  Kuo-Hsien Hsia,et al.  Multi-objective Optimization Using Fuzzy Logic for an Alpha-Beta Filter , 2013 .