Search

This paper deals with the robustness of the class of uncertain linear systems with Markovian jumping parameters (ULSMJP). The uncertainty is taken to be time-varying norm bounded. Under the assumptions of the boundedness of the uncertainties and the complete access to the system's state and its modes, a sufficient condition for stochastic stabilizability of this class of systems is established. An example is provided to demonstrate the usefulness of the proposed theoretical results.

The automatic classification of non stationary signals is an important practical goal in several domains. An essential classification task is to allocate the incoming signal to a group associated with the kind of physical phenomena producing it. In this paper, we present a modular system composed by three blocs: 1) Representation, 2) Dimensionality reduction and 3) Classification. The originality of our work consists in the use of a new wavelet called "Ben wavelet" in the representation stage. For the dimensionality reduction, we propose a new algorithm based on the random projection and the principal component analysis., {"references":["S. Abeysekera and B. Boashash, \"Methods of signal classification using\nthe images produced by Wigner distribution\" Pattern Recognition Letters, 12,\npp. 717-729, 1991.","L. Atlas, J. Droppo and J. McLaughlin, \"Optimizing time-frequency\ndistributions for automatic classification\" In the International Society for\nOptical Engineering, 1997.","M. Davy, C. Doncarli, and G. F. Boudreaux-Bartels, \"Improved\noptimization of time-frequency based signal classifiers\" IEEE Sig. Proc. Let,\n8, pp. 52-57, 2001.","F. Hlawasch and G. F. Boudreaux-Bartels, \"Linear and quadratic timefrequency\nsignal representations\" IEEE Sig. Proc. Mag, 9, pp. 21-67, 1992.","A. Papandreou-Suppappola, F. Hlawasch and G. Boudreaux-Bartels,\n\"Quadratic time-frequency representations with scale covariance and\ngeneralized time-shift covariance: a unified framework for the affine,\nhyperbolic and power classes\" Digital signal Processing, 8, pp.3-48, 1998.","L. Cohen, \"Generalized phase-space distribution functions\" J. Math. Phys,\n7, pp. 781-786, 1966.","L. Cohen, \"Time-frequency analysis\" Prentice Hall, 1995.","O. Rioul and P. Flandrin, \"Time-scale energy distributions : a general class\nextending wavelet transforms\" IEEE Trans on Signal Processing, 40, pp.\n1746-1757, 1992.","P. Flandrin, \"Temps-fréquence\", Academic Press, 1998.\n[10] F. Hlawasch, A. F. Papandreou-Suppappola and G. Boudreaux-Bartels,\n\"The power classes of quadratic time-frequency representations : a\ngeneralization of the hyperbolic and affine classes\" In 27th Asilomar Conf on\nSignals, Systems and computers, Pacific Grove, CA, 1265-1270, 1993.\n[11] F. Hlawasch, A. F. Papandreou-Suppappola and G. Boudreaux-Bartels,\n\"The hyperbolic class of quadratic time-frequency representations. Part II:\nSubclasses, intersection with affine and power classes, regularity unitarity\"\nIEEE Trans on Signal Processing, 45, pp. 303-315, 1997.\n[12] A. Papandreou-Suppappola, F. Hlawasch and G. Boudreaux-Bartels,\n\"Power class time-frequency representations: interference geometry,\nsmoothing and implementation\" In IEEE Symposium on Time-Frequency and\nTime-Scale Analysis, Paris, pp.193-196, 1996.\n[13] I. Daubechies, \"Ten lectures on wavelets\", SIAM, Philadelphia, Pa,\n1992.\n[14] C. Torrence and G. P. Compo, \"A practical guide to wavelet analysis\"\nBull. Amer. Meteor. Soc, 79, pp. 61-78, 1998.\n[15] M. Benbrahim, K. Benjelloun and A. Ibenbrahim, \"Discrimination des\nsignaux sismiques par réseaux de neurones artificiels\" In Proc of 3èmes\njournées nationales sur les systèmes intelligents: théorie et applications, Rabat,\nMorocco, pp. 62-66; 2004.\n[16] R. Bellman, \"Adaptive control processes: A guided tour\" Princeton\nUniversity Press, Princeton, 1961.\n[17] W.B. Johnson and J. Lindenstrauss, \"Extensions of Lipshitz mapping\ninto Hilbert space\" In Conference in modern analysis and probability, volume\n26 of Contemporary Mathematics, Amer. Math. Soc, pp. 189-206, 1984.\n[18] I. T. Jolliffe, \"Principal component analysis\", Springer-Verlag, 1986.\n[19] J. E. Jackson, \"A user's guide to principal components\", John Wiley,\nNew York, 1991.\n[20] M. Benbrahim, A. Daoudi, K. Benjelloun and A. Ibenbrahim,\n\"Discrimination of seismic signals using artificial neural networks\" In Proc of\nthe second world enformatika congress, WEC'05, Istanbul, Turkey, pp 4-7,\n2005.\n[21] A. Daoudi, M. Benbrahim and K. Benjelloun, \"An intelligent system to\nclassify leaks in water distribution pipes\" In Proc of the second world\nenformatika congress, WEC'05, Istanbul, Turkey, pp 1-3, 2005."]}