Sliding mode observer for estimating states and faults of linear time-delay systems with outputs subject to delays

Abstract In this paper, we study the problem of estimating states and faults for a class of linear time-delay systems using sliding mode observers. Both the states and outputs are subject to constant delays. This is a challenging problem and has not yet been resolved in the literature. By appropriately using a system transformation and the H ∞ filtering method, we propose a novel sliding mode observer scheme which can guarantee H ∞ asymptotic stability of the state and fault estimation errors. A numerical example is provided to illustrate the effectiveness of the new result.

[1]  Yuechao Ma,et al.  Integrated fault estimation and fault‐tolerant control for uncertain time‐varying delay nonlinear Markovian jump systems , 2018 .

[2]  Hui Li,et al.  Robust fast adaptive fault estimation for systems with time-varying interval delay , 2015, J. Frankl. Inst..

[3]  Arie Levant,et al.  Delay estimation via sliding mode for nonlinear time-delay systems , 2018, Autom..

[4]  Wen Chen,et al.  Fault Reconstruction and Fault-Tolerant Control via Learning Observers in Takagi–Sugeno Fuzzy Descriptor Systems With Time Delays , 2015, IEEE Transactions on Industrial Electronics.

[5]  Hieu Trinh,et al.  Stability Analysis of Nonlinear Time-Delay Systems Using a Novel Piecewise Positive Systems Method , 2018, IEEE Transactions on Automatic Control.

[6]  Rolf Isermann,et al.  Fault-diagnosis systems : an introduction from fault detection to fault tolerance , 2006 .

[7]  Hieu Minh Trinh,et al.  State and fault estimation for a class of non-infinitely observable descriptor systems using two sliding mode observers in cascade , 2019, J. Frankl. Inst..

[8]  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..

[9]  Emilia Fridman,et al.  Introduction to Time-Delay Systems: Analysis and Control , 2014 .

[10]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[11]  Hieu Minh Trinh,et al.  On ℓ1-gain control of 2-D positive Roesser systems with directional delays: Necessary and sufficient conditions , 2020, Autom..

[12]  Yan Peng,et al.  Stability analysis of linear systems with time-varying delay via intermediate polynomial-based functions , 2020, Autom..

[13]  Liu Hsu,et al.  Sliding mode observer for fault reconstruction of time-delay and sampled-output systems - a Time Shift Approach , 2019, Autom..

[14]  Emilia Fridman,et al.  Sampled-data sliding mode observer for robust fault reconstruction: A time-delay approach , 2014, J. Frankl. Inst..

[15]  Hieu Trinh,et al.  Robust state estimation for non-linear systems with unknown delays , 2019 .