References
- Alamo, T., Bravo, J., & Camacho, E. (2005). Guaranteed state estimation by zonotopes. Automatica, 41, 1035–1043.
- Assawinchaichote, W., Nguang, S., & Shi, P. (2007). Robust fuzzy filter design for uncertain nonlinear singularly perturbed systems with Markovian jumps: An LMI approach. Information Sciences, 177, 1699–1714.
- Bernard, O., & Gouzé, J. (2004). Closed loop observers bundle for uncertain biotechnological models. Journal of Process Control, 14, 765–774.
- Chang, K.W. (1972). Singular perturbations of a general boundary value problem. SIAM Journal on Mathematical Analysis, 3, 520–526.
- Chebotarev, S., Efimov, D., Raïssi, T., & Zolghadri, A. (2015). Interval observers for continuous-time LPV systems with L 1/L 2 performance. Automatica, 58, 82–89.
- Combastel, C., & Raka, S. (2011). A stable interval observer for LTI systems with no multiple poles. In IFAC World congress, Milan, Italy (Vol. 18, pp. 14335–14341).
- Efimov, D., Fridman, L., Raïssi, T., Zolghadri, A., & Seydou, R. (2012). Interval estimation for LPV systems applying high order sliding mode techniques. Automatica, 48, 2365–2371.
- Fang, T., Ghoshal, S., Jianhui, L., Biswas, G., Mahadevan, S., Jaw, L., & Navarra, K. (2007, March). PHM integration with maintenance and inventory management systems. In IEEE aerospace conference (pp. 1–12. MT: Big Sky).
- Fridman, E. (2001). State-feedback H∞ control of nonlinear singularly perturbed systems. International Journal of Robust and Nonlinear Control, 11, 1115–1125.
- Gennat, M., & Tibken, B. (2006). Guaranteed bounds for uncertain systems: Methods using linear Lyapunov-like functions, differential inequalities and a midpoint method. 12th GAMM-IMACS international symposium on Computer Arithmetic and Validated Numerics (pp. 17–17). Duisburg: IEEE.
- Gouzé, J., Rapaport, A., & Hadj-Sadok, M. (2000). Interval observers for uncertain biological systems. Ecological Modelling, 133, 45–56.
- Haddad, A. (1976). Linear filtering of singularly perturbed systems. IEEE Transactions on Automatic Control, 21, 515–519.
- Haddad, A., & Kokotovic, P. (1971). On a singular perturbation problem in linear filtering theory. Proceedings of 5th annual Princeton conference on Information Sciences and Systems, Princeton.
- Jaulin, L. (2002). Nonlinear bounded-error state estimation of continuous-time systems. Automatica, 38, 1079–1082.
- Jaulin, L., Kieffer, M., Didrit, O., & Walter, E. (2001). Applied interval analysis. London: Springer.
- Luo, J., Namburu, M., Pattipati, K., Qiao, L., Kawamoto, M., & Chigusa, S. (2003). Model-based prognostic techniques [maintenance applications]. Proceedings of systems readiness technology conference (pp. 330–340). Anaheim, CA: IEEE.
- Mazenc, F., & Bernard, O. (2010). Asymptotically stable interval observers for planar systems with complex poles. IEEE Transactions on Automatic Control, 55, 523–527.
- Mazenc, F., & Bernard, O. (2011). Interval observers for linear time-invariant systems with disturbances. Automatica, 47, 140–147.
- Mazenc, F., Dinh, T., & Niculescu, S. (2014). Interval observers for discrete-time systems. International Journal of Robust and Nonlinear Control, 24, 2867–2890.
- Moisan, M., & Bernard, O. (2006). Robust interval observers for uncertain chaotic systems. 45th IEEE conference on decision and control (pp. 3712–3717), San Diego, CA, USA.
- Moisan, M., Bernard, O., & Gouzé, J. (2009). Near optimal interval observers bundle for uncertain bioreactors. Automatica, 45, 291–295.
- Naidu, D. (2002). Singular perturbations and time scales in control theory and applications: An overview. Dynamics of Continuous Discrete and Impulsive Systems Series B, 9, 233–278.
- Nedialkov, N. (1999). Computing rigourous bounds on the solution of an initial value problem for an ordinary differential equation, PhD thesis. Toronto, Canada: University of Toronto.
- O’Reilly, J. (1979). Full-order observers for a class of singularly perturbed linear time-varying systems. International Journal of Control, 30, 745–756.
- Polyak, B.T., Nazin, S.A., Durieu, C., & Walter, E. (2004). Ellipsoidal parameter or state estimation under model uncertainty. Automatica, 40, 1171–1179.
- Raïssi, T., Efimov, D., & Zolghadri, A. (2012). Interval state estimation for a class of nonlinear systems. IEEE Transactions on Automatic Control, 57, 260–265.
- Raïssi, T., Ramdani, N., & Candau, Y. (2004). Set membership state and parameter estimation for systems described by nonlinear differential equations. Automatica, 40, 1771–1777.
- Rauch, H. (1974a). Application of singular perturbation to optimal estimation. 11th Annual Allerton conference on circuit and system theory (pp. 718–728), Monticello, IL.
- Rauch, H. (1974b). Order reduction in estimation with singular perturbation. 4th Symposium on nonlinear estimation theory and its applications (pp. 231–241), San Diego, CA.
- Reiss, E. (1980). A modified two-time method for the dynamic transitions of bifurcation. SIAM Journal on Applied Mathematics, 38, 249–260.
- Sankararaman, S., & Goebel, K. (2013). Remaining useful life estimation in prognostics: An uncertainty propagation problem. Proceedings of the AIAA Infotech@Aerospace conference, Boston, MA, USA.
- Sastry, S., & Desoer, C. (1981). Jump behavior of circuits and systems. IEEE Transactions on Circuits and Systems, 28, 1109–1124.
- Sebald, A., & Haddad, A. (1978). State estimation for singularly perturbed systems with uncertain perturbation parameter. IEEE Transactions on Automatic Control, 23, 464–469.
- Shen, X., & Deng, L. (1996). Decomposition solution of H∞ filter gain in singularly perturbed systems. Signal Processing, 55, 313–320.
- Smith, H. (1995). Monotone dynamical systems: An introduction to the theory of competitive and cooperative systems(Vol. 41). Mathematical surveys and monographs. American Mathematical Society.
- Teneketzis, D., & Sandell, N. (1977). Linear regulator design for stochastic systems by a multiple time-scales method. IEEE Transactions on Automatic Control, 22, 615–621.
- Tewa, J. (2007). Analyse globale des modèles épidémiologiques multi-compartimentaux: Application à des modèles intra-hôtes de paludisme et de VIH, PhD thesis. Université de Yaoundé.
- Wu, Y., Su, H., & Wu, Z. (2015). Filtering for discrete fuzzy stochastic systems with randomly occurred sensor nonlinearities. Signal Processing, 108, 288–296.
- Yousfi, B., Raïssi, T., Amairi, M., & Aoun, M. (2014). Interval observers design for singularly perturbed systems. 53rd IEEE conference on decision and control, Los Angeles, CA, USA (pp. 1637–1642).
- Yousfi, B., Raïssi, T., Amairi, M., & Aoun, M. (2015). Set-membership methodology for model-based systems prognosis. 9th IFAC symposium on fault detection, supervision and safety of technical processes, Paris, France.