Gain-scheduled / filtering for linear discrete-time systems with polytopic uncertainties

Abstract

The design of the gain-scheduled H₂/H_∞ filter for polytopic discrete-time systems is investigated. By introducing additional slack variables, a new mixed H₂/H_∞ performance criterion is proposed, which provides a decoupling between the Lyapunov matrix and system matrices. Based on the new performance criterion, a sufficient condition for the existence of the gain-scheduled H₂/H_∞ filter is derived. Furthermore, the filter design problem is converted into a convex optimization problem with linear matrix inequality (LMI) constraints. Simulation results show the effectiveness of the proposed approach.

References

1. Wang Z Huang B Robust H₂/H_∞ filtering for linear systems witherror variance constraintsIEEE Transactionson Signal Processing 2000 48(8)24632467. doi:10.1109/78.852028
2. Wang Z Unbehauen H Robust H₂/H_∞-state estimation for systems witherror variance constraints: the continuous-time caseIEEE Transactions on Automatic Control 1999 44(5)10611065. doi:10.1109/9.763229
3. Yang F Wang Z Hung Y S et al.Mixed H₂/H_∞ filtering for uncertain systems with regional pole assignmentIEEE Transactions on Aerospace and Electronic Systems 2005 41(2)438448. doi:10.1109/TAES.2005.1468739
4. Yang F Hung Y S Robust mixed H₂/H_∞ filteringwith regional pole assignment for uncertain discrete-time systemsIEEE Transactions on Circuits and Systems - I: FundamentalTheory and Applications 2002 49(8)12361241. doi:10.1109/TCSI.2002.801267
5. Palhares R M Peres P L D LMI approach to the mixed H₂/H_∞ filteringdesign for discrete-time uncertain systemsIEEE Transactions on Aerospace and Electronic Systems 2001 37(1)292296. doi:10.1109/7.913689
6. Gao H Lam J Xie L et al.New approach to mixed H₂/H_∞ filtering for polytopic discrete-time systemsIEEE Transactions on Signal Processing 2005 53(8)31833192. doi:10.1109/TSP.2005.851116
7. Montagner V F Oliveira R C L F Leite V J S et al.LMI approach for H_∞ linear parameter-varying state feedbackcontrolIn: IEE Proceedings of Control Theoryand Applications 2005 152(2)195201. doi:10.1049/ip‐cta:20045117
8. Goncalves E N Palhares R M Takahashi R H C Multi-objective optimization applied to robust H₂/H_∞ state-feedbackcontrol synthesisIn: Proceedings of the2004 American Control ConferenceNew YorkIEEE Press 2004 546194624
9. Yu L RobustControl-Linear Matrix Inequality MethodBeijingTsinghua University Press 2002 (in Chinese)
10. Mehdi D Boukas E K Bachelier O Static output feedback design for uncertain linear discrete-timesystemsIMA Journal of Mathematical Controland Information 2004 21(1)113. doi:10.1093/imamci/21.1.1
11. He L Wu A Duan G Improved robust mixed H₂/H_∞ filtering for uncertain continuous-time systemsIn: Proceedings of the 6th World Congress on IntelligentControl and AutomationNew YorkIEEE Press 2006 324122416
12. Apkarian P Tuan H D Bernussou J Continuous-time analysis, eigenstructure assignment, and H₂ synthesis withenhanced linear matrix inequalities (LMI) characterizationsIEEE Transactions on Automatic Control 2001 46(12)19411946. doi:10.1109/9.975496