Dissipativity analysis and synthesis for positive Roesser systems under the switched mechanism and Takagi-Sugeno fuzzy rules

Abstract This paper addresses the dissipativity analysis and controller design for a class of T-S fuzzy positive systems which are described by the Roesser model. First, sufficient conditions obtained by utilizing the minimum dwell time method and co-positive Lyapunov function approach are given to guarantee the considered system is 2-D ( ζ , η )- α -dissipative. Then via the state feedback fuzzy controller and the static output feedback fuzzy controller, criteria are also presented under which the resulting closed-loop systems are positive and 2-D ( ζ , η )- α -dissipative. Moreover, the explicit design schemes for the desired controller parameters are also presented in the form of linear programming. Finally, a simple illustrative example is provided to show the validity of the approach outlined in this article.

[1]  James Lam,et al.  Static output-feedback stabilization with optimal L1-gain for positive linear systems , 2016, Autom..

[2]  Shouming Zhong,et al.  Extended dissipative estimator design for uncertain switched delayed neural networks via a novel triple integral inequality , 2018, Appl. Math. Comput..

[3]  J. Willems.  Dissipative dynamical systems Part II: Linear systems with quadratic supply rates , 1972 .

[4]  Abdesselem Boulkroune,et al.  Adaptive Fuzzy Backstepping Tracking Control for Strict-Feedback Systems With Input Delay , 2017, IEEE Transactions on Fuzzy Systems.

[5]  Ligang Wu,et al.  Filtering and Control for Classes of Two-Dimensional Systems , 2015 .

[6]  W. Marszalek.  Two-dimensional state-space discrete models for hyperbolic partial differential equations , 1984 .

[7]  T. Kaczorek.  Positive 1D and 2D Systems , 2001 .

[8]  Jinling Liang,et al.  Stability analysis and synthesis for switched Takagi-Sugeno fuzzy positive systems described by the Roesser model , 2019, Fuzzy Sets Syst..

[9]  Xiang Yang,et al.  Dissipative-based sampled-data synchronization control for complex dynamical networks with time-varying delay , 2017, J. Frankl. Inst..

[10]  Hieu Minh Trinh,et al.  Stability analysis of two-dimensional Markovian jump state-delayed systems in the Roesser model with uncertain transition probabilities , 2016, Inf. Sci..

[11]  Ahmed El Hajjaji,et al.  Stabilisation of discrete 2D time switching systems by state feedback control , 2011, Int. J. Syst. Sci..

[12]  Magdi S. Mahmoud,et al.  Dissipativity analysis and design for uncertain Markovian jump systems with time-varying delays , 2013, Appl. Math. Comput..

[13]  strong,et al.  A Novel Framework Of Theory On Dissipative Systems , 2013 .

[14]  Hai Lin,et al.  On l1 stability of switched positive singular systems with time‐varying delay , 2017 .

[15]  Jian Xiao,et al.  Dissipativity and dwell time specifications of switched discrete-time systems and its applications in H∞ and robust passive control , 2015, Inf. Sci..

[16]  Gang Feng,et al.  Analysis and Synthesis of Fuzzy Control Systems , 2010 .

[17]  K. Teo,et al.  Sampled-data-based dissipative control of T-S fuzzy systems , 2019, Applied Mathematical Modelling.

[18]  Jie Tao,et al.  Filtering of two-dimensional periodic Roesser systems subject to dissipativity , 2018, Inf. Sci..

[19]  Weighted‐average ℓ1 filtering for switched positive systems , 2017 .

[20]  Guanghui Wen,et al.  Dissipativity based fault detection for 2D Markov jump systems with asynchronous modes , 2019, Autom..

[21]  Xiaojie Su,et al.  Finite-region dissipative dynamic output feedback control for 2-D FM systems with missing measurements , 2020, Inf. Sci..

[22]  Shouming Zhong,et al.  Dissipativity and passivity analysis for memristor-based neural networks with leakage and two additive time-varying delays , 2018, Neurocomputing.

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

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

[25]  Ligang Wu,et al.  Stability analysis and stabilization of 2-D switched systems under arbitrary and restricted switchings , 2015, Autom..

[26]  Jun Zhao,et al.  Dissipativity of positive switched systems using multiple linear supply rates , 2019, Nonlinear Analysis: Hybrid Systems.

[27]  Peng Shi,et al.  Two-Dimensional Dissipative Control and Filtering for Roesser Model , 2015, IEEE Transactions on Automatic Control.

[28]  Jun Shen.  Analysis and Synthesis of Dynamic Systems with Positive Characteristics , 2017 .

[29]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[30]  Hao Shen,et al.  Non-fragile extended dissipativity-based state feedback control for 2-D Markov jump delayed systems , 2019, Appl. Math. Comput..

[31]  Jinling Wang,et al.  Robust finite-horizon stability and stabilization for positive switched FM-II model with actuator saturation , 2020 .

[32]  Shengyuan Xu,et al.  Robust output feedback stabilization for two-dimensional continuous systems in roesser form , 2004, Appl. Math. Lett..

[33]  Tingwen Huang,et al.  l1 filtering for continuous-discrete T-S fuzzy positive Roesser model , 2018, J. Frankl. Inst..

[34]  Hui Gao,et al.  Non-fragile finite-time extended dissipative control for a class of uncertain discrete time switched linear systems , 2018, J. Frankl. Inst..

[35]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[36]  Jinling Wang,et al.  Dynamic output-feedback control for positive Roesser system under the switched and T-S fuzzy rules , 2018, Inf. Sci..

[37]  Jun Cheng,et al.  A new approach to generalized dissipativity analysis for fuzzy systems with coupling memory sampled-data control , 2020, Appl. Math. Comput..

[38]  Yong He,et al.  New results on dissipativity analysis of singular systems with time-varying delay , 2019, Inf. Sci..

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

[40]  Graziano Chesi,et al.  Robust stability and performance analysis of 2D mixed continuous-discrete-time systems with uncertainty , 2016, Autom..

[41]  Do Duc Thuan,et al.  Robust stability and robust stabilizability for periodically switched linear systems , 2019, Appl. Math. Comput..

[42]  Peng Shi,et al.  Stability of switched positive linear systems with average dwell time switching , 2012, Autom..

[43]  Grace S. Deaecto,et al.  Dynamic output feedback H∞ control of continuous-time switched affine systems , 2016, Autom..

[44]  Zhengrong Xiang,et al.  Robust state feedback $$H_\infty $$H∞ control for uncertain 2-D continuous state delayed systems in the Roesser model , 2016, Multidimens. Syst. Signal Process..

[45]  Jianbin Qiu,et al.  T-S fuzzy-model-based piecewise H∞ output feedback controller design for networked nonlinear systems with medium access constraint , 2014, Fuzzy Sets Syst..

[46]  Atreyee Kundu.  A new condition for stability of switched linear systems under restricted minimum dwell time switching , 2020, Syst. Control. Lett..