Unknown input interval observers for discrete-time linear switched systems

Abstract This paper deals with unknown input interval observer synthesis for discrete-time switched systems. First, a decomposition leading to obtain a subsystem not affected by the unknown input is presented. Second, an interval observer is designed based on the Input-to-State Stability (ISS). The gains are computed by solving Linear Matrix Inequalities (LMI) formulated based on multiple quadratic Lyapunov functions under average dwell time switching signals. In addition, a change of coordinates can be taken in order to ensure the positivity of the estimation errors. Finally, an explicit expression for the unknown input bounds is derived. Note that while the additive disturbances and the measurement noises are unknown but assumed to be bounded with known bounds, the unknown input signals are neither bounded nor stochastic.

[1]  Saïd Mammar,et al.  Robust interval observer for switched systems with unknown inputs: Application to vehicle dynamics estimation , 2018, Eur. J. Control.

[2]  Denis V. Efimov,et al.  Interval State Estimation for a Class of Nonlinear Systems , 2012, IEEE Transactions on Automatic Control.

[3]  Frédéric Mazenc,et al.  Interval observer composed of observers for nonlinear systems , 2014, 2014 European Control Conference (ECC).

[4]  Alfredo Germani,et al.  A New Approach to Design Interval Observers for Linear Systems , 2015, IEEE Transactions on Automatic Control.

[5]  Tarek Raïssi,et al.  A note on interval observer design for unknown input estimation , 2016, Int. J. Control.

[6]  Leonid M. Fridman,et al.  State Estimation for Linear Switched Systems with Unknown Inputs , 2012, ADHS.

[7]  Sanghyuk Lee,et al.  Observers for bilinear systems with unknown inputs and application to superheater temperature control , 1997 .

[8]  Thach Ngoc Dinh.  Interval observer and Positive observer , 2014 .

[9]  Julien Marzat,et al.  Interval observer design for unknown input estimation of linear time-invariant discrete-time systems , 2017 .

[10]  Yan Song,et al.  Robust MPC under event-triggered mechanism and Round-Robin protocol: An average dwell-time approach , 2018, Inf. Sci..

[11]  David Henry,et al.  An unknown input interval observer for LPV systems under L2-gain and L∞-gain criteria , 2019, Autom..

[12]  Jun Huang,et al.  Further Result on Interval Observer Design for Discrete-Time Switched Systems and Application to Circuit Systems , 2020, IEEE Transactions on Circuits and Systems II: Express Briefs.

[13]  Tarek Raïssi,et al.  Interval observer design for continuous-time switched systems under known switching and unknown inputs , 2018, Int. J. Control.

[14]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[15]  Zhao Ping,et al.  Input-to-state stability of discrete-time switched nonlinear systems , 2017, 2017 29th Chinese Control And Decision Conference (CCDC).

[16]  Zhiwei Gao,et al.  Unknown Input Observer-Based Robust Fault Estimation for Systems Corrupted by Partially Decoupled Disturbances , 2016, IEEE Transactions on Industrial Electronics.

[17]  Yi Shen,et al.  Interval observer design for uncertain discrete-time linear systems , 2018, Syst. Control. Lett..

[18]  Olivier Bernard,et al.  Interval observers for linear time-invariant systems with disturbances , 2011, Autom..

[19]  Gregery T. Buzzard,et al.  State and Unknown Input Observers for Nonlinear Systems With Bounded Exogenous Inputs , 2017, IEEE Transactions on Automatic Control.

[20]  F. Mazenc,et al.  Interval observers for discrete‐time systems , 2014 .

[21]  J. Gouzé,et al.  Interval observers for uncertain biological systems , 2000 .

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

[23]  Tarek Raïssi,et al.  Interval estimation for discrete-time LPV switched systems , 2019, 2019 IEEE 58th Conference on Decision and Control (CDC).

[24]  Hiroshi Ito,et al.  Interval observers for global feedback control of nonlinear systems with robustness with respect to disturbances , 2017, Eur. J. Control.

[25]  Shreyas Sundaram,et al.  State and unknown input observers for discrete-time nonlinear systems , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[26]  Hiroshi Ito,et al.  Decentralized interval observer-based control for a class of nonlinear systems , 2016, 2016 55th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE).

[27]  Hiroshi Ito,et al.  Interval observers for continuous-time bilinear systems with discrete-time outputs , 2016, 2016 European Control Conference (ECC).

[28]  Tarek Raïssi,et al.  Optimal interval observers for discrete-time linear switched systems , 2020, Int. J. Control.

[29]  Tarek Raïssi,et al.  Interval Estimation for Discrete-Time Switched Linear Systems Based on L∞ Observer and Ellipsoid Analysis , 2021, IEEE Control Systems Letters.

[30]  Denis V. Efimov,et al.  Control of Nonlinear and LPV Systems: Interval Observer-Based Framework , 2013, IEEE Transactions on Automatic Control.

[31]  Denis V. Efimov,et al.  Interval estimation for continuous-time switched linear systems , 2018, Autom..

[32]  Yi Shen,et al.  A state augmentation approach to interval fault estimation for descriptor systems , 2020, Eur. J. Control.

[33]  Bin Jiang,et al.  An adaptive technique for robust diagnosis of faults with independent effects on system outputs , 2002 .

[34]  Denis V. Efimov,et al.  Interval Observers for Time-Varying Discrete-Time Systems , 2013, IEEE Transactions on Automatic Control.

[35]  G. Millerioux,et al.  Unknown input observers for switched linear discrete time systems , 2004, Proceedings of the 2004 American Control Conference.

[36]  M. Saif,et al.  A novel approach to the design of unknown input observers , 1991 .

[37]  Mohammad Khajenejad,et al.  Simultaneous Input and State Interval Observers for Nonlinear Systems with Full-Rank Direct Feedthrough , 2020, 2020 59th IEEE Conference on Decision and Control (CDC).

[38]  Wei Xie,et al.  Control of non-linear switched systems with average dwell time: interval observer-based framework , 2016 .

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

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

[41]  Alexander S. Poznyak,et al.  Unknown Input and State Estimation for Unobservable Systems , 2009, SIAM J. Control. Optim..

[42]  Didier Maquin,et al.  Estimation of unknown inputs in linear systems , 1994, Proceedings of 1994 American Control Conference - ACC '94.