Reduced-Order Observer Design for Switched Descriptor Systems With Unknown Inputs

This paper presents a systematical reduced-order observer design method for a class of switched descriptor systems containing unknown inputs (UIs) in both the dynamic and the output equations. Generally speaking, when the output of the system contains UIs, the reduced-order observer design will become much more challenging. In order to overcome the difficulty brought by the UIs in the output, first, by introducing a new UI vector, a new equivalent system is obtained, which does not contain UIs in the corresponding output any more. Then, for the purpose of reduced-order observer design, the observer matching condition (OMC) and the minimal phase condition (MPC) are discussed, and it is shown that the new general system maintains both the OMC and the MPC. Subsequently, based on the discussions on the existence conditions, a reduced-order unknown input observer is developed to asymptotically estimate the state of the original system. Finally, an electronic circuit example is given to show the effectiveness of the proposed method.

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

[2]  Michael Defoort,et al.  Fault detection based on higher-order sliding mode observer for a class of switched linear systems , 2015 .

[3]  Jun Li,et al.  Discrete-time linear descriptor system unknown input observer design: an auxiliary output-based approach , 2017 .

[4]  Donghua Zhou,et al.  A novel sliding mode observer for state and fault estimation in systems not satisfying matching and minimum phase conditions , 2017, Autom..

[5]  Okyay Kaynak,et al.  Sliding Mode Observer-Based FTC for Markovian Jump Systems With Actuator and Sensor Faults , 2017, IEEE Transactions on Automatic Control.

[6]  Fanglai Zhu,et al.  On the observer matching condition and unknown input observer design based on the system left-invertibility concept , 2018, Trans. Inst. Meas. Control.

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

[8]  Fanglai Zhu,et al.  Observer Design and Unknown Input Reconstruction for a Class of Switched Descriptor Systems , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[9]  Stefen Hui,et al.  Sliding-mode observers for systems with unknown inputs: A high-gain approach , 2010, Autom..

[10]  Fanglai Zhu,et al.  Output control of MIMO system with unmatched disturbance based on high-order unknown input observer , 2017 .

[11]  R. W. Wilde,et al.  Observers for linear systems with unknown inputs , 1988 .

[12]  Damien Koenig,et al.  Unknown input proportional multiple-integral observer design for linear descriptor systems: application to state and fault estimation , 2005, IEEE Transactions on Automatic Control.

[13]  Xin Wang,et al.  Active Mode Identification and Continuous State Estimation for Switched Linear Systems with Unknown Inputs and Slow Switching Signal , 2015, Circuits Syst. Signal Process..

[14]  Fanglai Zhu,et al.  Observer-based output consensus of a class of heterogeneous multi-agent systems with unmatched disturbances , 2018, Commun. Nonlinear Sci. Numer. Simul..

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

[16]  Tianyou Chai,et al.  Dwell-Time-Based Observer Design for Unknown Input Switched Linear Systems Without Requiring Strong Detectability of Subsystems , 2017, IEEE Transactions on Automatic Control.

[17]  B. Marx,et al.  Hα-filtering and state feedback control for discrete-time switched descriptor systems , 2009 .

[18]  Yonggui Kao,et al.  Stability and Stabilization for Singular Switching Semi-Markovian Jump Systems With Generally Uncertain Transition Rates , 2018, IEEE Transactions on Automatic Control.

[19]  Daniel W. C. Ho,et al.  State/noise estimator for descriptor systems with application to sensor fault diagnosis , 2006, IEEE Transactions on Signal Processing.

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

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

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

[23]  Shengyuan Xu,et al.  Actuator fault estimation for discrete-time switched systems with finite-frequency , 2017, Syst. Control. Lett..

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

[25]  Peng Shi,et al.  New Results on Stability of Slowly Switched Systems: A Multiple Discontinuous Lyapunov Function Approach , 2017, IEEE Transactions on Automatic Control.

[26]  Xudong Zhao,et al.  Robust impulsive reset observers of a class of switched nonlinear systems with unknown inputs , 2017, J. Frankl. Inst..

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

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

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

[30]  Hamid Reza Karimi,et al.  Robust estimator design for switched systems with unknown switching time: An LMI-based approach , 2018, Eur. J. Control.