Uncertain 2D Continuous Systems with State Delay: Filter Design using an Polynomial Approach

This paper proposes a methodology to design filters that extract information from noisy signals. From a mathematical point of view, a method is used based on homogeneous polynomially parameter-dependent (HPPD) matrices of arbitrary degree. The optimal H filter is then obtained by solving a convex optimization problem using off-the-self software. To show the effectiveness of the proposed filter design methodology some examples are solved, and the solution is illustrated using computer simulations.

[1]  Huijun Gao,et al.  A delay-dependent approach to robust H∞ filtering for uncertain discrete-time state-delayed systems , 2004, IEEE Trans. Signal Process..

[2]  Uri Shaked,et al.  H/sub infinity /-minimum error state estimation of linear stationary processes , 1990 .

[3]  U. Shaked,et al.  Game theory approach to optimal linear state estimation and its relation to the minimum H/sub infinity /-norm estimation , 1992 .

[4]  B. Zhang,et al.  Oscillation criteria of a class of partial difference equations with delays , 2004 .

[5]  M.N.S. Swamy,et al.  A new method for computing the stability margin of two-dimensional continuous systems , 2002 .

[6]  Abdelaziz Hmamed,et al.  Robust H∞ filtering for uncertain 2-D continuous systems, based on a polynomially parameter-dependent Lyapunov function , 2011, The 2011 International Workshop on Multidimensional (nD) Systems.

[7]  Isaac Yaesh,et al.  Robust H∞ filtering of stationary continuous-time linear systems with stochastic uncertainties , 2001, IEEE Trans. Autom. Control..

[8]  Abdelaziz Hmamed,et al.  Robust ∞ Filtering of 2D Roesser Discrete Systems: A Polynomial Approach , 2012 .

[9]  Huijun Gao,et al.  Robust - Filtering for Uncertain Systems with Multiple Time-Varying State Delays , 2003 .

[10]  Abdellah Benzaouia,et al.  Stabilization of 2D saturated systems by state feedback control , 2010, Multidimens. Syst. Signal Process..

[11]  Jianhua Huang,et al.  Existence of traveling wave fronts of delayed lattice differential equations , 2004 .

[12]  Pramod P. Khargonekar,et al.  FILTERING AND SMOOTHING IN AN H" SETTING , 1991 .

[13]  Luo An,et al.  PID-Fuzzy Control Method with Time Delay Compensation for Hybrid Active Power Filter with Injection Circuit , 2011 .

[14]  Pedro Luis Dias Peres,et al.  Robust 𝒽∞ filtering for uncertain discrete-time state-delayed systems , 2001, IEEE Trans. Signal Process..

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

[16]  Minyue Fu,et al.  Interpolation approach to H ∞ estimation and its interconnection to loop transfer recovery , 1991 .

[17]  F. F. G. Areed,et al.  Design of Neuro-Fuzzy Controller for a Rotary Dryer , 2012 .

[18]  J. Speyer,et al.  A Linear-Quadratic Game Approach to Estimation and Smoothing , 1991, 1991 American Control Conference.

[19]  U. Shaked,et al.  Game theory approach to optimal linear estimation in the minimum H/sup infinity /-norm sense , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[20]  C. Tian,et al.  Stability criteria for a class of linear delay partial difference equations , 1999 .

[21]  Mansour Souissi,et al.  Takagi-Sugeno Fuzzy Observer Design for Induction Motors with Immeasurable Decision Variables: State Estimation and Sensor Fault Detection , 2011 .

[22]  Lihua Xie,et al.  H ∞ filtering for a class of uncertain nonlinear systems , 1993 .

[23]  A. Hmamed,et al.  Robust stabilization under linear fractional parametric uncertainties of two-dimensional systems with Roesser models , 2008 .

[24]  Leang-San Shieh,et al.  Modeling and solution of two-dimensional input time-delay system , 2002, J. Frankl. Inst..

[25]  Ricardo C. L. F. Oliveira,et al.  LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions , 2006, Syst. Control. Lett..

[26]  Zhiping Lin,et al.  Robust H Filtering for Uncertain 2-D Continuous Systems , 2005 .

[27]  Krzysztof Galkowski,et al.  Delay differential control theory applied to differential linear repetitive processes , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[28]  I. Yaesh,et al.  Game theory approach to optimal linear estimation in minimum H_∞-norm sense , 1989 .

[29]  Mohammed Alfidi,et al.  LMI Conditions for Robust Stability of 2D Linear Discrete-Time Systems , 2008 .

[30]  Akansha Mehrotra,et al.  A Novel Algorithm for Impulse Noise Removal and Edge Detection , 2012 .

[31]  Nagaratna P. Hegde,et al.  Robust Speech Processing in EW Environment , 2012 .

[32]  Lihua Xie,et al.  H∞ deconvolution filtering of 2-d digital systems , 2002, IEEE Trans. Signal Process..

[33]  Shengyuan Xu,et al.  H∞ Control of 2 D linear state-delayed systems , 2003 .

[34]  Shengyuan Xu,et al.  Robust H ∞ filtering for a class of non-linear systems with state delay and parameter uncertainty , 2002 .

[35]  Krzysztof Galkowski,et al.  LMI based stability analysis for 2D continuous systems , 2002, 9th International Conference on Electronics, Circuits and Systems.

[36]  Wojciech Paszke,et al.  Robust H/sub /spl infin// filtering for Uncertain2-D continuous systems , 2005, IEEE Transactions on Signal Processing.