Filtering and ℓ1-gain analysis for 2-D positive system with Markov jump parameters

In this paper, the ℓ1-gain performance is analyzed for the two-dimensional (2-D) Markov jump positive systems, which is generalized from the well-known Roesser model. Our attention is focused on designing a full-order filter for the 2-D positive system such that the filtering error system is stochastically asymptotically stable with ℓ1-gain index. In terms of the linear programming approach, sufficient conditions are established for the existence and explicit design of the desired filter. Finally, an illustrative example is presented to show effectiveness of the proposed methods.

[1]  Hailiang Yang,et al.  Exponential stabilizability of stochastic systems with Markovian jumping parameters , 1999, Autom..

[2]  Huijun Gao,et al.  I filtering for 2D Markovian jump systems , 2008, Autom..

[3]  Huijun Gao,et al.  Stabilization and H∞ control of two-dimensional Markovian jump systems , 2004, IMA J. Math. Control. Inf..

[4]  Tadeusz Kaczorek,et al.  Reachability and controllability of 2D positive linear systems with state feedbacks , 1999 .

[5]  P. E. Wellstead,et al.  Two-dimensional and EM techniques for cross directional estimation and control , 2002 .

[6]  Mohammed Alfidi,et al.  Controller synthesis for positive 2D systems described by the Roesser model , 2008, 2008 47th IEEE Conference on Decision and Control.

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

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

[9]  Qing-Long Han,et al.  I1-gain performance analysis and positive filter design for positive discrete-time Markov jump linear systems: A linear programming approach , 2014, Autom..

[10]  Hamid Reza Karimi,et al.  Delay-dependent exponential stabilization of positive 2D switched state-delayed systems in the Roesser model , 2014, Inf. Sci..

[11]  H. Chizeck,et al.  Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control , 1990 .

[12]  Donghua Zhou,et al.  H ∞ filtering for non-linear systems with stochastic sensor saturations and Markov time delays: the asymptotic stability in probability , 2016 .

[13]  Ahmed Alsaedi,et al.  Distributed H∞ state estimation for stochastic delayed 2-D systems with randomly varying nonlinearities over saturated sensor networks , 2016, Inf. Sci..

[14]  Mauro Bisiacco.  New results in 2D optimal control theory , 1995, Multidimens. Syst. Signal Process..

[15]  Jian Shen,et al.  Stability and positive observer design for positive 2D discrete-time system with multiple delays , 2017, Int. J. Syst. Sci..

[16]  Xingwen Liu,et al.  Stability Criterion of 2‐D Positive Systems with Unbounded Delays Described by Roesser Model , 2015 .

[17]  H. Trinh,et al.  Delay-dependent stability and stabilisation of two-dimensional positive Markov jump systems with delays , 2017 .

[18]  Zidong Wang,et al.  Pinning controllability of autonomous Boolean control networks , 2016, Science China Information Sciences.

[19]  Guang-Ren Duan,et al.  Robust H∞ filter design for 2D discrete systems in Roesser model , 2008, Int. J. Autom. Comput..

[20]  James Lam,et al.  $H_{\infty}$ Positive Filtering for Positive Linear Discrete-Time Systems: An Augmentation Approach , 2010, IEEE Transactions on Automatic Control.

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

[22]  Huijun Gao,et al.  Filtering for uncertain 2-D discrete systems with state delays , 2007, Signal Process..

[23]  Hailiang Yang,et al.  Technical Communique: Exponential stabilizability of stochastic systems with Markovian jumping parameters> >>altfn>This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Editor Peter Dorato. , 1999 .

[24]  Shengyuan Xu,et al.  Robust H∞ Filtering for a Class of Nonlinear Discrete-Time Markovian Jump Systems , 2004 .

[25]  Zidong Wang,et al.  State estimation for two‐dimensional complex networks with randomly occurring nonlinearities and randomly varying sensor delays , 2014 .