Finite-frequency memory filter design for uncertain linear discrete-time systems: A polynomially parameter-dependent approach.

This paper investigates the robust filtering problem for linear uncertain systems affected by noises in restricted frequency intervals. Different from traditional filter schemes, a finite-frequency memory filter is designed to generalize conventional memoryless ones in such a way that a sequence of latest output measurements are employed for current estimation. To be specific, a memory filter is sought which ensures that for all admissible uncertainties, the filtering error system is asymptotically stable with a prescribed noise-attenuation level in the restricted frequency range. To accomplish this, the finite-frequency specification is characterized by the generalized Kalman-Yakubovich-Popov (KYP) lemma, aiming at improving the capability of noise-attenuation over the given frequency range. Moreover, the homogeneous polynomially parameter-dependent technique is adopted to facilitate filter design and reduce conservatism further. Based on the proposed scheme, we prove rigorously that additional past output measurements contribute to less conservative results. Finally, a quarter-car model with an active-suspension system is used to validate the proposed scheme.

[1]  José Claudio Geromel,et al.  I robust filter design with performance certificate via convex programming , 2008, Autom..

[2]  Edoardo Mosca,et al.  Robust H2 and Hinfinity filtering for uncertain linear systems , 2006, Autom..

[3]  Heng Wang,et al.  Integrated fault detection and control for LPV systems , 2009 .

[4]  Wen-An Zhang,et al.  A New Observer-Based Cooperative Fault-Tolerant Tracking Control Method With Application to Networked Multiaxis Motion Control System , 2021, IEEE Transactions on Industrial Electronics.

[5]  José Claudio Geromel,et al.  Analysis and Synthesis of Robust Control Systems Using Linear Parameter Dependent Lyapunov Functions , 2006, IEEE Transactions on Automatic Control.

[6]  Alexander Shapiro,et al.  First and second order analysis of nonlinear semidefinite programs , 1997, Math. Program..

[7]  Jianghai Hu,et al.  Sequential parametric convex approximation algorithm for bilinear matrix inequality problem , 2019, Optim. Lett..

[8]  Fuwen Yang,et al.  Adaptive Event-Triggered Transmission Scheme and $H_{\infty}$ Filtering Co-Design Over a Filtering Network With Switching Topology , 2019, IEEE Transactions on Cybernetics.

[9]  Huaicheng Yan,et al.  Input–output finite-time mean square stabilization of nonlinear semi-Markovian jump systems , 2019, Automatica.

[10]  Huijun Gao,et al.  Finite Frequency H∞ Control for Vehicle Active Suspension Systems , 2011 .

[11]  Ricardo C. L. F. Oliveira,et al.  Robust H∞ filter design with past output measurements for uncertain discrete-time systems , 2016, Autom..

[12]  Li Yu,et al.  Analysis and Synthesis of Switched Time-Delay Systems: The Average Dwell Time Approach , 2018 .

[13]  Meng Wang,et al.  A Novel Piecewise Affine Filtering Design for T–S Fuzzy Affine Systems Using Past Output Measurements , 2020, IEEE Transactions on Cybernetics.

[14]  Wojciech Paszke,et al.  Finite frequency range iterative learning fault-tolerant control for discrete time-delay uncertain systems with actuator faults. , 2019, ISA transactions.

[15]  Jun Cheng,et al.  New results on H∞ filtering for Markov jump systems with uncertain transition rates. , 2017, ISA transactions.

[16]  Sing Kiong Nguang,et al.  Distributed Filtering for Discrete-Time T–S Fuzzy Systems With Incomplete Measurements , 2018, IEEE Transactions on Fuzzy Systems.

[17]  Yung-Shan Chou,et al.  Robust H-infinity filtering in finite frequency domain for polytopic systems with application to in-band quantisation noise reduction in uncertain cascaded sigma-delta modulators , 2012 .

[18]  Meng Wang,et al.  Finite Frequency Filtering Design for Uncertain Discrete-Time Systems Using Past Output Measurements , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[20]  Qing-Long Han,et al.  Robust Hinfinity filtering for a class of uncertain linear systems with time-varying delay , 2008, Autom..

[21]  Tetsuya Hiyama,et al.  Response properties of atmospheric turbulence measurement instruments using Russian research aircraft , 2004 .

[22]  Ricardo C. L. F. Oliveira,et al.  Parameter-Dependent LMIs in Robust Analysis: Characterization of Homogeneous Polynomially Parameter-Dependent Solutions Via LMI Relaxations , 2007, IEEE Transactions on Automatic Control.

[23]  R.H.C. Takahashi,et al.  H/sub 2//H/sub /spl infin// filter design for systems with polytope-bounded uncertainty , 2006, IEEE Transactions on Signal Processing.

[24]  Jin-Hua She,et al.  Improved bounded-real-lemma representation and H∞ control of systems with polytopic uncertainties , 2005, IEEE Trans. Circuits Syst. II Express Briefs.

[25]  Ricardo H. C. Takahashi,et al.  H2/H∞ filter design for systems with polytope-bounded uncertainty , 2006 .

[26]  Dong Hwan Lee.  An improved finite frequency approach to robust H∞ filter design for LTI systems with polytopic uncertainties , 2013 .

[27]  Shinji Hara,et al.  Generalized KYP lemma: unified frequency domain inequalities with design applications , 2005, IEEE Transactions on Automatic Control.

[28]  Kaixiang Peng,et al.  Fault detection for piecewise affine systems with application to ship propulsion systems. , 2017, ISA transactions.

[29]  Guang-Hong Yang,et al.  A finite frequency approach to filter design for uncertain discrete‐time systems , 2008 .

[30]  Huijun Gao,et al.  Robust finite frequency Hinfinity filtering for uncertain 2-D Roesser systems , 2012, Autom..

[31]  P. Gahinet,et al.  Affine parameter-dependent Lyapunov functions and real parametric uncertainty , 1996, IEEE Trans. Autom. Control..

[32]  Meng Wang,et al.  Finite Frequency Memory Output Feedback Controller Design for T–S Fuzzy Dynamical Systems , 2018, IEEE Transactions on Fuzzy Systems.

[33]  Hamid Reza Karimi,et al.  A linear matrix inequality approach to robust fault detection filter design of linear systems with mixed time-varying delays and nonlinear perturbations , 2010, J. Frankl. Inst..

[34]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[35]  Huijun Gao,et al.  Finite Frequency $H_{\infty }$ Control for Vehicle Active Suspension Systems , 2011, IEEE Transactions on Control Systems Technology.

[36]  Hong Wang,et al.  Fault Estimation for a Class of Nonlinear Systems Based on Intermediate Estimator , 2016, IEEE Transactions on Automatic Control.

[37]  Qing Li,et al.  Robust finite‐frequency filter design for linear uncertain systems using polynomially parameter‐dependent approach , 2020, IET Control Theory & Applications.

[38]  David Zhang,et al.  Improved robust H2 and Hinfinity filtering for uncertain discrete-time systems , 2004, Autom..

[39]  D. McFarlane,et al.  Optimal guaranteed cost control and filtering for uncertain linear systems , 1994, IEEE Trans. Autom. Control..

[40]  Young Hoon Joo,et al.  Periodically Time-Varying ${\cal H}_{\infty}$ Memory Filter Design for Discrete-Time LTI Systems With Polytopic Uncertainty , 2014, IEEE Transactions on Automatic Control.