Observer Design and Unknown Input Reconstruction for a Class of Switched Descriptor Systems

This correspondence paper is concerned with observer design problems for a class of unknown input switched descriptor systems under average dwell time switching signals. The switched descriptor system under consideration is first transformed into a general switched linear system, and then a switched reduced-order observer that can asymptotically estimate the system state without suffering the influence from the unknown inputs is developed. Besides, a high-order sliding mode observer is introduced to obtain the estimations of the output derivatives by using the system measured outputs. On the basis of estimations of the states and output derivatives, an unknown input reconstructing method is provided. Finally, two examples are presented to verify the effectiveness of the proposed approaches.

[1]  M. Darouach,et al.  Full-order observers for linear systems with unknown inputs , 1994, IEEE Trans. Autom. Control..

[2]  Antonio Ramírez-Treviño,et al.  On the observer design problem for continuous-time switched linear systems with unknown switchings , 2015, J. Frankl. Inst..

[3]  Mehrdad Saif,et al.  Fuzzy Nonlinear Unknown Input Observer Design with Fault Diagnosis Applications , 2010 .

[4]  Hamid Reza Karimi,et al.  Fault detection for continuous‐time switched systems under asynchronous switching , 2014 .

[5]  Shen Yin,et al.  Switching Stabilization for a Class of Slowly Switched Systems , 2015, IEEE Transactions on Automatic Control.

[6]  Vincent Cocquempot,et al.  Observer-based fault tolerant control for hybrid impulsive systems. , 2010 .

[7]  J. Lam,et al.  Equivalence of several characteristics of dual switched linear systems , 2014 .

[8]  Michael Defoort,et al.  Hybrid sliding mode observer for switched linear systems with unknown inputs , 2014, J. Frankl. Inst..

[9]  Guoliang Wang,et al.  Passive Control of Switched Singular Systems via Output Feedback , 2015 .

[10]  Alessandro Pisano,et al.  Finite-time converging jump observer for switched linear systems with unknown inputs ☆ , 2011 .

[11]  Peng Shi,et al.  Non-weighted quasi-time-dependent H∞ filtering for switched linear systems with persistent dwell-time , 2015, Autom..

[12]  Xiaohang Li,et al.  Nonfragile Fault-Tolerant Fuzzy Observer-Based Controller Design for Nonlinear Systems , 2016, IEEE Transactions on Fuzzy Systems.

[13]  Alessandro Pisano,et al.  Switched Observers for Switched Linear Systems With Unknown Inputs , 2011, IEEE Transactions on Automatic Control.

[14]  Jie Chen,et al.  Design of unknown input observers and robust fault detection filters , 1996 .

[15]  R. Shorten,et al.  On dimensionality reduction and the stability of a class of switched descriptor systems , 2013, Autom..

[16]  Junqi Yang,et al.  Simultaneous state and output disturbance estimations for a class of switched linear systems with unknown inputs , 2017, Int. J. Syst. Sci..

[17]  Horacio J. Marquez,et al.  A novel approach to unknown input filter design for discrete-time linear systems , 2014, Autom..

[18]  Martin J. Corless,et al.  State and Input Estimation for a Class of Uncertain Systems , 1998, Autom..

[19]  Arie Levant,et al.  Higher-order sliding modes, differentiation and output-feedback control , 2003 .

[20]  Bin Meng,et al.  Reachability conditions for switched linear singular systems , 2006, IEEE Transactions on Automatic Control.

[21]  A. Levant.  Robust exact differentiation via sliding mode technique , 1998 .

[22]  Zhengzhi Han,et al.  A note on observers for Lipschitz nonlinear systems , 2002, IEEE Trans. Autom. Control..

[23]  Leonid M. Fridman,et al.  Second-order sliding-mode observer for mechanical systems , 2005, IEEE Transactions on Automatic Control.

[24]  Qingling Zhang,et al.  Hybrid impulsive control for switched singular systems , 2011 .

[25]  Damien Koenig,et al.  Filtering and fault estimation of descriptor switched systems , 2016, Autom..

[26]  Shovan Bhaumik,et al.  Full- and reduced-order observer design for rectangular descriptor systems with unknown inputs , 2015, J. Frankl. Inst..

[27]  Hao Liu,et al.  Multiple-Mode Observer Design for a Class of Switched Linear Systems , 2015, IEEE Transactions on Automation Science and Engineering.

[28]  Shreyas Sundaram,et al.  On Delayed Observers for Linear Systems with Unknown Inputs , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[29]  Damien Koenig,et al.  Unknown Input Observers for Switched Nonlinear Discrete Time Descriptor Systems , 2008, IEEE Transactions on Automatic Control.

[30]  Asier Ibeas,et al.  Switched nonlinear singular systems with time‐delay: Stability analysis , 2015 .

[31]  Shaocheng Tong,et al.  Observed-Based Adaptive Fuzzy Decentralized Tracking Control for Switched Uncertain Nonlinear Large-Scale Systems With Dead Zones , 2016, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[32]  Zhifeng Gao,et al.  Observers design for switched discrete-time singular time-delay systems with unknown inputs , 2015 .

[33]  Hak-Keung Lam,et al.  Adaptive Sliding Mode Control for Interval Type-2 Fuzzy Systems , 2016, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[34]  R. Giral,et al.  Current-Mode Control of a Coupled-Inductor Buck–Boost DC–DC Switching Converter , 2012, IEEE Transactions on Power Electronics.

[35]  Denis V. Efimov,et al.  Continuous and discrete state estimation for switched LPV systems using parameter identification , 2015, Autom..

[36]  Stefen Hui,et al.  Stress estimation using unknown input observer , 2013, 2013 American Control Conference.

[37]  Wu-Hua Chen,et al.  A revisit to the design of switched observers for switched linear systems with unknown inputs , 2014 .

[38]  Fanglai Zhu,et al.  State estimation and unknown input reconstruction via both reduced-order and high-order sliding mode observers☆ , 2012 .

[39]  Leonid M. Fridman,et al.  State exact reconstruction for switched linear systems via a super-twisting algorithm , 2011, Int. J. Syst. Sci..

[40]  Damien Koenig,et al.  Observer design for unknown input nonlinear descriptor systems via convex optimization , 2006, IEEE Transactions on Automatic Control.

[41]  Hamid Reza Karimi,et al.  Robust Observer Design for Unknown Inputs Takagi–Sugeno Models , 2013, IEEE Transactions on Fuzzy Systems.

[42]  Zhifeng Gao,et al.  Functional observer for switched discrete-time singular systems with time delays and unknown inputs , 2015 .

[43]  MengChu Zhou,et al.  A New Class of Petri Nets for Modeling and Property Verification of Switched Stochastic Systems , 2015, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[44]  Zairui Gao,et al.  H-infinity control for a class of uncertain switched descriptor systems , 2015, 2015 Chinese Automation Congress (CAC).

[45]  François Guerin,et al.  Hybrid Modeling for Performance Evaluation of Multisource Renewable Energy Systems , 2011, IEEE Transactions on Automation Science and Engineering.

[46]  Leonid M. Fridman,et al.  High-order sliding modes observers for linear autonomous-switched systems with unknown inputs , 2012, 2012 12th International Workshop on Variable Structure Systems.

[47]  Jaime A. Moreno,et al.  Strict Lyapunov Functions for the Super-Twisting Algorithm , 2012, IEEE Transactions on Automatic Control.