New LMI Conditions for Reduced-order Observer of Lipschitz Discrete-time Systems: Numerical and Experimental Results

The objective of this paper is to propose a reduced-order observer for a class of Lipschitz nonlinear discrete-time systems. The conditions that guarantee the existence of this observer are presented in the form of linear matrix inequalities (LMIs). To handle the Lipschitz nonlinearities, the Lipschitz condition and the Young′s relation are adequately operated to add more degrees of freedom to the proposed LMI. Necessary and sufficient conditions for the existence of the unbiased reduced-order observer are given. An extension to H∞ performance analysis is considered in order to deal with H∞ asymptotic stability of the estimation error in the presence of disturbances that affect the state of the system. To highlight the effectiveness of the proposed design methodology, three numerical examples are considered. Then, high performances are shown through real time implementation using the ARDUINO MEGA 2560 device.

[1]  Michel Zasadzinski,et al.  H∞ circle criterion observer design for Lipschitz nonlinear systems with enhanced LMI conditions , 2016, 2016 American Control Conference (ACC).

[2]  H. Trinh,et al.  On the Existence and Design of Functional Observers for Linear Systems , 2007, 2007 International Conference on Mechatronics and Automation.

[3]  R. Rajamani.  Observers for Lipschitz nonlinear systems , 1998, IEEE Trans. Autom. Control..

[4]  Mohamed Boutayeb,et al.  A strong tracking extended Kalman observer for nonlinear discrete-time systems , 1999, IEEE Trans. Autom. Control..

[5]  H. Trinh,et al.  Design of unknown input functional observers for nonlinear systems with application to fault diagnosis , 2013 .

[6]  Karim Dahech,et al.  A sliding mode observer for uncertain nonlinear systems based on multiple models approach , 2017, Int. J. Autom. Comput..

[7]  Jhon A. Isaza-Hurtado,et al.  State Estimation Using Non-uniform and Delayed Information: A Review , 2018, Int. J. Autom. Comput..

[8]  Francesco Amato,et al.  Functional observers design for descriptor systems via LMI: Continuous and discrete-time cases , 2017, Autom..

[9]  H. Souley Ali,et al.  H ∞ functional filtering for stochastic bilinear systems with multiplicative noises , 2009 .

[10]  Sliding Mode Functional Observers for Nonlinear Systems , 2008, 2008 IEEE Region 10 and the Third international Conference on Industrial and Information Systems.

[11]  A. Alessandri.  Design of observers for lipschitz nonlinear systems using LMI , 2004 .

[12]  Wei Zhang,et al.  State estimation for discrete-time systems with generalized Lipschitz nonlinear dynamics , 2015, Advances in Difference Equations.

[13]  M. Abbaszadeh,et al.  Nonlinear observer design for one-sided Lipschitz systems , 2010, Proceedings of the 2010 American Control Conference.

[14]  M. Darouach,et al.  Functional Observers Design for Two Interconnected Linear Systems Via LMI , 2011 .

[15]  Michel Zasadzinski,et al.  Convex optimization based dual gain observer design for Lipschitz nonlinear systems , 2016, 2016 American Control Conference (ACC).

[16]  Piyapong Niamsup,et al.  Robust Finite-time H∞ Control of Linear Time-varying Delay Systems with Bounded Control via Riccati Equations , 2018, Int. J. Autom. Comput..

[17]  Michel Zasadzinski,et al.  Hinfinity functional filtering for stochastic bilinear systems with multiplicative noises , 2009, Autom..

[18]  Mohamed Darouach,et al.  Functional observers for linear descriptor systems , 2009, 2009 17th Mediterranean Conference on Control and Automation.

[19]  Zhengtao Ding,et al.  Consensus Control of a Class of Lipschitz Nonlinear Systems With Input Delay , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  H. Trinh.  Linear functional state observer for time-delay systems , 1999 .

[21]  Seyed Hassan Zabihifar,et al.  Adaptive Fuzzy Sliding Mode Control of Under-actuated Nonlinear Systems , 2018, Int. J. Autom. Comput..