Novel ISS criteria for digital filters using generalized overflow non-linearities and external interference

Sufficient criteria for input-to-state stability (ISS) of fixed-point state-space interfered digital filters with generalized overflow non-linearities are presented. The generalized overflow non-linearities under consideration cover the usual types of overflow arithmetic employed in practice, such as saturation, zeroing, two’s complement and triangular. The criteria not only ensure diminishing consequence of external interference but also confirm the asymptotic stability of the system when external interference disappears. The criteria are derived in the linear matrix inequality (LMI) framework. Simulation results are provided to illustrate the utility of the presented approach. With the help of one example, it is illustrated that the presented approach can lead to a less stringent ISS condition for the digital filters with saturation non-linearities compared with a previously reported approach.

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

[2]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[3]  Haranath Kar,et al.  LMI-based criterion for the robust stability of 2D discrete state-delayed systems using generalized overflow nonlinearities , 2011 .

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

[5]  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.

[6]  Eduardo Sontag.  Input to State Stability: Basic Concepts and Results , 2008 .

[7]  V. Krishna Rao Kandanvli,et al.  A Delay-Dependent Approach to Stability of Uncertain Discrete-Time State-Delayed Systems with Generalized Overflow Nonlinearities , 2012 .

[8]  R. Olfati-Saber,et al.  Distributed Kalman Filter with Embedded Consensus Filters , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[9]  V. Krishna Rao Kandanvli,et al.  Robust stability of discrete-time state-delayed systems employing generalized overflow nonlinearities , 2008 .

[10]  Choon Ki Ahn.  A new LMI criterion for the realization of limit cycle-free direct form digital filters with saturation arithmetic , 2012 .

[11]  A. Isidori,et al.  Disturbance attenuation and H/sub infinity /-control via measurement feedback in nonlinear systems , 1992 .

[12]  Hamid Reza Karimi,et al.  On integral input-to-state stability for a feedback interconnection of parameterised discrete-time systems , 2016, Int. J. Syst. Sci..

[13]  Vimal Singh.  Stability of discrete-time systems joined with a saturation operator on the state-space: Generalized form of Liu-Michel's criterion , 2011, Autom..

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

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

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

[17]  Vimal Singh,et al.  Robust stability of 2-D discrete systems described by the Fornasini-Marchesini second model employing quantization/overflow nonlinearities , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[18]  M. James,et al.  Extending H-infinity Control to Nonlinear Systems: Control of Nonlinear Systems to Achieve Performance Objectives , 1987 .

[19]  A. Astolfi.  Disturbance Attenuation and H,-Control Via Measurement Feedback in , 1992 .

[20]  Choon Ki Ahn.  Two new criteria for the realization of interfered digital filters utilizing saturation overflow nonlinearity , 2014, Signal Process..

[21]  Priyanka Kokil,et al.  Asymptotic Stability of Fixed-Point State-Space Digital Filters with Saturation Arithmetic and External Disturbance: An IOSS Approach , 2015, Circuits Syst. Signal Process..

[22]  C. Ahn,et al.  Unbiased Finite Impluse Response Filtering: An Iterative Alternative to Kalman Filtering Ignoring Noise and Initial Conditions , 2017, IEEE Control Systems.

[23]  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..

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

[25]  Vimal Singh.  Global asymptotic stability of 2-D state-space digital filters with saturation arithmetic: Modified approach , 2008, Signal Process..

[26]  Haranath Kar,et al.  Robust stability of 2-D discrete systems employing generalized overflow nonlinearities: An LMI approach , 2011, Digit. Signal Process..

[27]  Eduardo Sontag.  Comments on integral variants of ISS , 1998 .

[28]  Reza Olfati-Saber,et al.  Kalman-Consensus Filter : Optimality, stability, and performance , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[29]  Moritz Diehl,et al.  Robust Stability of Moving Horizon Estimation Under Bounded Disturbances , 2016, IEEE Transactions on Automatic Control.

[30]  Haranath Kar.  A new sufficient condition for the global asymptotic stability of 2-D state-space digital filters with saturation arithmetic , 2008, Signal Process..

[31]  Choon Ki Ahn.  $l_{2} - l_{\infty}$ Elimination of Overflow Oscillations in 2-D Digital Filters Described by Roesser Model With External Interference , 2013, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

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

[34]  Philippe Martin,et al.  Invariant Extended Kalman Filter: theory and application to a velocity-aided attitude estimation problem , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

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

[36]  João Pedro Hespanha,et al.  Equivalent Characterizations of Input-to-State Stability for Stochastic Discrete-Time Systems , 2014, IEEE Transactions on Automatic Control.

[37]  Reza Olfati-Saber,et al.  Distributed Kalman filtering for sensor networks , 2007, 2007 46th IEEE Conference on Decision and Control.

[38]  J. Tsinias.  Input to state stability properties of nonlinear systems and applications to bounded feedback stabilization using saturation , 1997 .

[39]  Choon Ki Ahn.  A new condition for the elimination of overflow oscillations in direct form digital filters , 2012 .

[40]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

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

[42]  A. Morse,et al.  Certainty equivalence implies detectability , 1998 .

[43]  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 .

[44]  M. Grimble,et al.  A New Approach to the H ∞ Design of Optimal Digital Linear Filters , 1989 .

[45]  Xunyuan Yin,et al.  Distributed output‐feedback fault detection and isolation of cascade process networks , 2017 .

[46]  Riccardo Marino,et al.  Nonlinear output feedback tracking with almost disturbance decoupling , 1999, IEEE Trans. Autom. Control..

[47]  Xunyuan Yin,et al.  Distributed moving horizon state estimation of two-time-scale nonlinear systems , 2017, Autom..

[48]  Haranath Kar,et al.  An improved criterion for the global asymptotic stability of fixed-point state-space digital filters with combinations of quantization and overflow , 2014, Digit. Signal Process..

[49]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

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

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

[52]  Xiaoguang Qi,et al.  Some results on difference polynomials sharing values , 2012, Advances in Difference Equations.

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

[54]  Priyanka Kokil,et al.  A note on the criterion for the elimination of overflow oscillations in fixed-point digital filters with saturation arithmetic and external disturbance , 2012 .

[55]  Eduardo Sontag,et al.  Input-to-state stability for discrete-time nonlinear systems , 1999, at - Automatisierungstechnik.

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

[57]  Choon Ki Ahn.  IOSS Criterion for the Absence of Limit Cycles in Interfered Digital Filters Employing Saturation Overflow Arithmetic , 2013, Circuits Syst. Signal Process..

[58]  Henry Cox,et al.  On the estimation of state variables and parameters for noisy dynamic systems , 1964 .

[59]  Ning Sun,et al.  Improved criterion for the elimination of overflow oscillations in digital filters with external disturbance , 2012 .