Amato, Francesco; Ariola, Marco; Cosentino, Carlo Finite-time stabilization via dynamic output feedback. (English) Zbl 1099.93042 Automatica 42, No. 2, 337-342 (2006). Summary: The finite-time stabilization of continuous-time linear systems is considered; this problem has been previously solved in the state feedback case. In this work the assumption that the state is available for feedback is removed and the output feedback problem is investigated. The main result provided is a sufficient condition for the design of a dynamic output feedback controller which makes the closed loop system finite-time stable. Such sufficient condition is given in terms of an LMI optimization problem; this gives the opportunity of fitting the finite-time control problem in the general framework of the LMI approach to the multi-objective synthesis. In this context an example illustrates the design of a controller which guarantees, at the same time, finite-time stability together with some pole placement requirements. Cited in 125 Documents MSC: 93D21 Adaptive or robust stabilization 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory 93B52 Feedback control Keywords:LMIs; output feedback; finite-time stability PDFBibTeX XMLCite \textit{F. Amato} et al., Automatica 42, No. 2, 337--342 (2006; Zbl 1099.93042) Full Text: DOI References: [1] Amato, F., Ariola, M., & Dorato, P. (1999). Robust finite-time stabilization of linear uncertain systems via gain-scheduled output feedback. In Proceedings of the 14th IFAC World Congress; Amato, F., Ariola, M., & Dorato, P. (1999). Robust finite-time stabilization of linear uncertain systems via gain-scheduled output feedback. In Proceedings of the 14th IFAC World Congress [2] Amato, F.; Ariola, M.; Dorato, P., Finite time control of linear systems subject to parametric uncertainties and disturbances, Automatica, 37, 1459-1463 (2001) · Zbl 0983.93060 [3] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory (1994), SIAM Press: SIAM Press Philadelphia · Zbl 0816.93004 [4] Chilali, M.; Gahinet, P.; Apkarian, P., Robust pole placement in LMI regions, IEEE Transactions on Automatic Control, 44, 2257-2270 (1999) · Zbl 1136.93352 [5] D’Angelo, H., Linear time-varying systems: Analysis and synthesis (1970), Allyn & Bacon: Allyn & Bacon Newton · Zbl 0202.08502 [6] Dorato, P. (1961). Short time stability in linear time-varying systems. In Proceedings of IRE International Convention Record Part 4; Dorato, P. (1961). Short time stability in linear time-varying systems. In Proceedings of IRE International Convention Record Part 4 [7] Gottfried, B. S.; Weisman, J., Introduction to optimization theory (1973), Prentice-Hall: Prentice-Hall Englewoods Cliffs [8] Stevens, B. L.; Lewis, F. L., Aircraft control and simulation (1992), Wiley: Wiley New York · Zbl 0749.93035 [9] Weiss, L.; Infante, E. F., Finite time stability under perturbing forces and on product spaces, IEEE Transactions on Automatic Control, 12, 54-59 (1967) · Zbl 0168.33903 [10] Zhou, K.; Doyle, J. C., Essentials of robust control (1998), Prentice-Hall: Prentice-Hall Upper Saddle River, NJ This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.