Geometric tools for solving the FDI problem for linear periodic discrete-time systems

References

• Anderson, B., & Moore, J. (1981). Time-varying feedback laws for decentralised control. IEEE Transactions on Automatic Control, 26, 1133–1139.
   Web of Science ®Google Scholar
• Andrzej, W. (1987). Robust stabilization of uncertain systems by periodic feedback. International Journal of Control, 45, 747–758.
   Web of Science ®Google Scholar
• Araki, M., & Yamamoto, K. (1986). Multivariable multirate sampled-data systems: State-space description, transfer characteristics, and Nyquist criterion. IEEE Transactions on Automatic Control, 31, 145–154.
   Web of Science ®Google Scholar
• Basile, G., & Marro, G. (1969). Controlled and conditioned invariant subspaces in linear system theory. Journal of Optimization Theory and Applications, 3, 306–315.
   Google Scholar
• Basile, G., & Marro, G. (1992). Controlled and conditioned invariants in linear system theory. Englewood Cliffs, NJ: Prentice Hall.
   Google Scholar
• Berg, M., Amit, N., & Powell, J. (1988). Multirate digital control system design. IEEE Transactions on Automatic Control, 33, 1139–1150.
   Web of Science ®Google Scholar
• Bittanti, S. (1986). Deterministic and stochastic linear periodic systems. Time Series and Linear Systems, 141–182.
   Google Scholar
• Bittanti, S., & Colaneri, P. (2008). Periodic systems: Filtering and control. London, UK: Springer Verlag.
   Google Scholar
• Bittanti, S., & Guardabassi, G. (1986). Optimal periodic control and periodic systems analysis: An overview. 25th IEEE Conference on Decision and Control (25, pp. 1417–1423).
   Google Scholar
• Davis, J. (1972). Stability conditions derived from spectral theory: Discrete systems with periodic feedback. SIAM Journal on Control, 10, 1–13.
   Web of Science ®Google Scholar
• De Persis, C., & Isidori, A. (2001). A geometric approach to nonlinear fault detection and isolation. IEEE Transactions on Automatic Control, 46, 853–865.
   Web of Science ®Google Scholar
• Fadali, M.S., Colaneri, P., & Nel, M. (2003). H2 robust fault estimation for periodic systems. Proceedings of the American Control Conference (pp. 2973–2978).
   Google Scholar
• Fadali, M.S., & Gummuluri, S. (2001). Robust observer-based fault detection for periodic systems. Proceedings of the American Control Conference (pp. 464–469).
   Google Scholar
• Ferrara Jr, E. (1985). Frequency-domain implementations of periodically time-varying filters. IEEE Transactions on Acoustics, Speech and Signal Processing, 33, 883–892.
   Google Scholar
• Francis, B., & Georgiou, T. (1988). Stability theory for linear time-invariant plants with periodic digital controllers. IEEE Transactions on Automatic Control, 33, 820–832.
   Web of Science ®Google Scholar
• Galeani, S., Menini, L., & Potini, A. (2012). Robust trajectory tracking for a class of hybrid systems: An internal model principle approach. IEEE Transactions on Automatic Control, 57, 344–359.
   Web of Science ®Google Scholar
• Galeani, S., Menini, L., Potini, A., & Tornambè, A. (2008). Trajectory tracking for a particle in elliptical billiards. International Journal of Control, 81, 189–213.
   Web of Science ®Google Scholar
• Galeani, S., Menini, L., & Tornambè, A. (2004). Dynamic stabilizing controllers for LTI systems and multirate control. IEE Proceedings in Control Theory and Automation, 151, 739–744.
   Web of Science ®Google Scholar
• Grasselli, O.M., & Longhi, S. (1986). Disturbance localization with dead-beat control for linear periodic discrete-time systems. International Journal of Control, 44, 1319–1347.
   Web of Science ®Google Scholar
• Grasselli, O.M., & Longhi, S. (1987). Linear function dead-beat observers with disturbance localization for linear periodic discrete-time systems. International Journal of Control, 45, 1603–1626.
   Web of Science ®Google Scholar
• Grasselli, O.M., & Longhi, S. (1988). Disturbance localization by measurement feedback for linear periodic discrete-time systems. Automatica, 24, 375–385.
   Web of Science ®Google Scholar
• Grasselli, O.M., & Longhi, S. (1988). Zeros and poles of linear periodic multivariable discrete-time systems. Circuits, Systems, and Signal Processing, 7, 361–380.
   Web of Science ®Google Scholar
• Grasselli, O.M., & Longhi, S. (1991). The geometric approach for linear periodic discrete-time systems. Linear Algebra and Its Applications, 158, 27–60.
   Web of Science ®Google Scholar
• Grasselli, O.M., & Longhi, S. (1991). Pole placement for nonreachable periodic discrete-time systems. Mathematics of Control, Signals and Systems, 4, 439–455.
   Web of Science ®Google Scholar
• Grasselli, O., Isidori, A., & Nicolò, F. (1979). Output regulation of a class of bilinear systems under constant disturbances. Automatica, 15, 189–195.
   Web of Science ®Google Scholar
• Grasselli, O., Isidori, A., & Nicolò, F. (1980). Dead-beat control of discrete-time bilinear systems. International Journal of Control, 32, 31–39.
   Web of Science ®Google Scholar
• Grasselli, O., & Longhi, S. (1989). Eigenvalue assignment for linear periodic discrete-time non-reachable systems. IEEE International Conference on Control and Applications (pp. 707–712).
   Google Scholar
• Grasselli, O., & Longhi, S. (1991). Input and output decoupling zeros of linear periodic discrete-time systems. Kybernetika, 27, 202–212.
   Web of Science ®Google Scholar
• Grasselli, O., & Longhi, S. (1993). Block decoupling with stability of linear periodic systems. Journal of Mathematical Systems, Estimation and Control, 3, 427–458.
   Google Scholar
• Helmke, U., & Verriest, E.I. (2011). Structure and parametrization of periodic linear systems. Mathematics of Control, Signals and Systems, 23, 67–99.
   Web of Science ®Google Scholar
• Isidori, A., Krener, A., Gori-Giorgi, C., & Monaco, S. (1981). Nonlinear decoupling via feedback: A differential geometric approach. IEEE Transactions on Automatic Control, 26, 331–345.
   Web of Science ®Google Scholar
• Kaczorek, T. (1985). Pole placement for linear discrete-time systems by periodic output feedbacks. Systems & Control Letters, 6, 267–269.
   Web of Science ®Google Scholar
• Khargonekar, P., Poolla, K., & Tannenbaum, A. (1985). Robust control of linear time-invariant plants using periodic compensation. IEEE Transactions on Automatic Control, 30, 1088–1096.
   Web of Science ®Google Scholar
• Longhi, S., & Monteriù, A. (2009). Fault detection for linear periodic systems using a geometric approach. IEEE Transactions on Automatic Control, 54, 1637–1643.
   Web of Science ®Google Scholar
• Longhi, S., & Monteriù, A. (2010). A geometric approach to fault detection and isolation problem for linear periodic systems. 49th IEEE Conference on Decision and Control (pp. 7724–7729).
   Google Scholar
• Massoumnia, M.A. (1986). A geometric approach to the synthesis of failure detection filters. IEEE Transactions on Automatic Control, 31, 839–846.
   Web of Science ®Google Scholar
• Massoumnia, M.A., Verghese, G.C., & Willsky, A.S. (1989). Failure detection and identification. IEEE Transactions on Automatic Control, 34, 316–321.
   Web of Science ®Google Scholar
• Menini, L., & Tornambè, A. (2001). Asymptotic tracking of periodic trajectories for a simple mechanical system subject to non-smooth impacts. IEEE Transactions on Automatic Control, 46, 1122–1126.
   Web of Science ®Google Scholar
• Meyer, R., & Burrus, C. (1975). A unified analysis of multirate and periodically time-varying digital filters. IEEE Transactions on Circuits and Systems, 22, 162–168.
   Google Scholar
• Perdon, A., Conte, G., & Longhi, S. (1992). Invertibility and inversion of linear periodic systems. Automatica, 28, 645–648.
   Web of Science ®Google Scholar
• Richards, J. (1983). Analysis of periodically time-varying systems, Communications and control engineering series. Berlin: Springer-Verlag.
   Google Scholar
• Varga, A. (2007). An overview of recent developments in computational methods for periodic systems. Periodic Control Systems (3, pp. 157–162).
   Google Scholar
• Vlach, J., Singhal, K., & Vlach, M. (1984). Computer oriented formulation of equations and analysis of switched-capacitor networks. IEEE Transactions on Circuits and Systems, 31, 753–765.
   Google Scholar
• Wonham, W.M. (1979). Linear multivariable control: A geometric approach (Vol. 10). New York: Springer-Verlag, Inc.(Applications of Mathematics).
   Google Scholar
• Zhang, P., Ding, S.X., Wang, G.Z., & Zhou, D.H. (2005). Fault detection of linear discrete-time periodic systems. IEEE Transactions on Automatic Control, 50, 239–244.
   Web of Science ®Google Scholar
• Zhang, P., Ding, S., & Liu, P. (2012). A lifting based approach to observer based fault detection of linear periodic systems. IEEE Transactions on Automatic Control, 57, 457–462.
   Web of Science ®Google Scholar