A New Delay-Dependent Stability Criterion for Uncertain 2-D Discrete Systems Described by Roesser Model Under the Influence of Quantization/Overflow Nonlinearities

This paper considers the problem of global asymptotic stability of a class of two-dimensional uncertain discrete systems described by the Roesser model under the influence of various combinations of quantization/overflow nonlinearities and interval-like time-varying delay in the state. The systems under consideration involve parameter uncertainties that are assumed to be deterministic and norm-bounded. A delay-dependent stability criterion is derived by estimating the forward difference of the Lyapunov functional based on the reciprocally convex approach. Examples are provided to illustrate the effectiveness of the proposed criterion.

[1]  Peter H. Bauer,et al.  A stability analysis of two-dimensional nonlinear digital state-space filters , 1990, IEEE Trans. Acoust. Speech Signal Process..

[2]  Vladimir L. Kharitonov,et al.  Time-Delay Systems , 2013 .

[3]  Tamal Bose.  Asymptotic stability of two-dimensional digital filters under quantization , 1994, IEEE Trans. Signal Process..

[4]  Ettore Fornasini,et al.  A 2-D systems approach to river pollution modelling , 1991, Multidimens. Syst. Signal Process..

[5]  Qing-Long Han,et al.  Improved stability criteria and controller design for linear neutral systems , 2009, Autom..

[6]  K. K. Pang,et al.  Design criterion for zero-input asymptotic overflow-stability of recursive digital filters in the presence of quantization , 1985 .

[7]  Choon Ki Ahn.  Two-dimensional digital filters described by Roesser model with interference attenuation , 2013, Digit. Signal Process..

[8]  Xiefu Jiang,et al.  Stability criteria for linear discrete-time systems with interval-like time-varying delay , 2005, Proceedings of the 2005, American Control Conference, 2005..

[9]  Steffi Knorn,et al.  Stability of Two-Dimensional Linear Systems With Singularities on the Stability Boundary Using LMIs , 2013, IEEE Transactions on Automatic Control.

[10]  R. Roesser.  A discrete state-space model for linear image processing , 1975 .

[11]  M. Mahmoud.  Robust Control and Filtering for Time-Delay Systems , 2000 .

[12]  A. Michel,et al.  Stability analysis of state-space realizations for two-dimensional filters with overflow nonlinearities , 1994 .

[13]  Vimal Singh.  Improved LMI-based criterion for global asymptotic stability of 2-D state-space digital filters described by Roesser model using two's complement arithmetic , 2012, Digit. Signal Process..

[14]  Vimal Singh.  Improved Criterion for Global Asymptotic Stability of 2-D Discrete Systems With State Saturation , 2007, IEEE Signal Processing Letters.

[15]  V. Krishna Rao Kandanvli,et al.  Delay‐dependent LMI condition for global asymptotic stability of discrete‐time uncertain state‐delayed systems using quantization/overflow nonlinearities , 2011 .

[16]  Ettore Fornasini,et al.  Doubly-indexed dynamical systems: State-space models and structural properties , 1978, Mathematical systems theory.

[17]  Peter H. Bauer,et al.  Comments on "Stability and absence of overflow oscillations for 2-D discrete-time systems" , 1998, IEEE Trans. Signal Process..

[18]  Donghua Zhou,et al.  Robust delay dependent iterative learning fault-tolerant control for batch processes with state delay and actuator failures , 2012 .

[19]  Zhiping Lin,et al.  Non-fragile H2 and H∞ filter designs for polytopic two-dimensional systems in Roesser model , 2010, Multidimens. Syst. Signal Process..

[20]  David J. Hill,et al.  Stability and absence of overflow oscillations for 2-D discrete-time systems , 1996, IEEE Trans. Signal Process..

[21]  C. Peng,et al.  Improved delay-dependent stabilisation criteria for discrete systems with a new finite sum inequality , 2012 .

[22]  M. Malek-Zavarei,et al.  Time-Delay Systems: Analysis, Optimization and Applications , 1987 .

[23]  I-Kong Fong,et al.  Delay-dependent robust Hinfinity filtering for uncertain 2-D state-delayed systems , 2007, Signal Process..

[24]  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..

[25]  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..

[26]  Peter H. Bauer,et al.  Realization using the Roesser model for implementations in distributed grid sensor networks , 2011, 49th IEEE Conference on Decision and Control (CDC).

[27]  Tien-Lin Chang,et al.  Limit cycles in a two-dimensional first-order digital filter , 1977 .

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

[29]  R. Bracewell.  Two-dimensional imaging , 1994 .

[30]  G. Izuta.  Networked 2-d linear discrete feedback control systems design on the basis of observer controller , 2012, 2012 16th International Conference on System Theory, Control and Computing (ICSTCC).

[31]  Peter H. Bauer,et al.  Realization using the Roesser model for implementations in distributed grid sensor networks , 2011, Multidimens. Syst. Signal Process..

[32]  Vimal Singh,et al.  Stability analysis of 2-D state-space digital filters using Lyapunov function: a caution , 1997, IEEE Trans. Signal Process..

[33]  T. Malakorn.  Multidimensional Linear Systems and Robust Control , 2003 .

[34]  Donghua Zhou,et al.  Robust design of feedback integrated with iterative learning control for batch processes with uncertainties and interval time-varying delays , 2011 .

[35]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[36]  A. Willson.  Some effects of quantization and adder overflow on the forced response of digital filters , 1972 .

[37]  G. Feng,et al.  Improved approach to delay-dependent stability analysis of discrete-time systems with time-varying delay [Brief Paper] , 2010 .

[38]  N. El-Agizi,et al.  Two-dimensional digital filters with no overflow oscillations , 1979 .

[39]  Stanislaw Walczak,et al.  Application of 2D systems to investigation of a process of gas filtration , 2012, Multidimens. Syst. Signal Process..

[40]  Vimal Singh,et al.  Stability analysis of 2-D digital filters with saturation arithmetic: an LMI approach , 2005, IEEE Transactions on Signal Processing.

[41]  Zhengrong Xiang,et al.  Delay-dependent robust $$H_\infty $$ control for 2-D discrete nonlinear systems with state delays , 2014, Multidimens. Syst. Signal Process..

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

[43]  Haranath Kar,et al.  A note on the improved LMI-based criterion for global asymptotic stability of 2-D state-space digital filters described by Roesser model using two's complement overflow arithmetic , 2013, Digit. Signal Process..

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

[45]  T. Kaczorek.  Two-Dimensional Linear Systems , 1985 .

[46]  Spyros G. Tzafestas,et al.  Two-dimensional digital filters without overflow oscillations and instability due to finite word length , 1992, IEEE Trans. Signal Process..

[47]  Jianming Xu,et al.  Delay-dependent H∞ Control for Uncertain 2-D Discrete Systems with State Delay in the Roesser Model , 2013, Circuits Syst. Signal Process..

[48]  Xin-Ping Guan,et al.  H∞ filtering of 2-D discrete state-delayed systems , 2009, Multidimens. Syst. Signal Process..

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

[50]  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.

[51]  Shengyuan Xu,et al.  Robust stability and stabilisation of 2D discrete state-delayed systems , 2004, Syst. Control. Lett..

[52]  Shengyuan Xu,et al.  Delay-dependent stability condition for uncertain linear 2-D state-delayed systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[53]  Peter H. Bauer,et al.  A novel approach to grid sensor networks , 2008, 2008 15th IEEE International Conference on Electronics, Circuits and Systems.

[54]  Hj Hans Butterweck,et al.  Finite wordlength in digital filters: A review , 1988 .

[55]  Li Yu,et al.  Delay-dependent H∞ control for 2-D discrete state delay systems in the second FM model , 2009, Multidimens. Syst. Signal Process..

[56]  J. Liu,et al.  Note on stability of discrete-time time-varying delay systems , 2012 .

[57]  A. Venetsanopoulos,et al.  Design of 3-D Noncausal Filters with Small Roundoff Noise and No Overflow Oscillations , 1997, Proceedings of 13th International Conference on Digital Signal Processing.

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

[59]  M. Fahmy,et al.  Stability and overflow oscillations in 2-D state-space digital filters , 1981 .

[60]  Haranath Kar,et al.  LMI-based criterion for robust stability of 2-D discrete systems with interval time-varying delays employing quantisation / overflow nonlinearities , 2014, Multidimens. Syst. Signal Process..

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

[62]  Fuli Wang,et al.  Two‐dimensional dynamic PCA for batch process monitoring , 2005 .

[63]  Xin-Ping Guan,et al.  Output Feedback H∞ Control for 2-D State-Delayed Systems , 2009, Circuits Syst. Signal Process..

[64]  Priyanka Kokil,et al.  Stability of 2-D digital filters described by the Roesser model using any combination of quantization and overflow nonlinearities , 2012, Signal Process..

[65]  G. Marchesini,et al.  State-space realization theory of two-dimensional filters , 1976 .

[66]  V. Krishna Rao Kandanvli,et al.  An LMI condition for robust stability of discrete-time state-delayed systems using quantization/overflow nonlinearities , 2009, Signal Process..

[67]  Shyh-Feng Chen,et al.  Delay-dependent stability for 2D systems with time-varying delay subject to state saturation in the Roesser model , 2010, Appl. Math. Comput..

[68]  Thomas E Marlin,et al.  Process Control , 1995 .