Ilchmann, Achim; Owens, David H. Adaptive stabilization with exponential decay. (English) Zbl 0699.93071 Syst. Control Lett. 14, No. 5, 437-443 (1990). Summary: Adaptive high gain stabilizers for classes of linear time-invariant state space systems are presented. The classes cover multi-input-multi-output systems where the state dimension is not known. Only standard assumptions such as minimum phase and known respectively unknown sign are required. The main result is, that the adaptive control laws of C. I. Byrnes and J. C. Willems [“Adaptive stabilization of multivariable linear systems”, Proc. 23rd IEEE Conf., Decis. Control, Las Vegas/NV 1984, Vol. 3, 1574-1577 (New York 1984)] can be modified to produce a guarantee of exponentially decaying states. Cited in 7 Documents MSC: 93D15 Stabilization of systems by feedback 93C40 Adaptive control/observation systems 93C05 Linear systems in control theory 93C15 Control/observation systems governed by ordinary differential equations Keywords:Adaptive high gain stabilizers; time-invariant PDFBibTeX XMLCite \textit{A. Ilchmann} and \textit{D. H. Owens}, Syst. Control Lett. 14, No. 5, 437--443 (1990; Zbl 0699.93071) Full Text: DOI References: [1] Byrnes, C. I.; Willems, J. C., Adaptive stabilization of multivariable linear systems, (Proc. of the 23rd Conf. on Decision and Control. Proc. of the 23rd Conf. on Decision and Control, Las Vegas, NV (1984)), 1574-1577 [2] Hale, J., Theory of Functional Differential Equations (1977), Springer-Verlag: Springer-Verlag New York [3] Helmke, U.; Prätzel-Wolters, D., Stability and robustness properties of universal adaptive controllers for first order linear systems, Internat. J. Control, 48, 1153-1182 (1988) · Zbl 0671.93031 [4] Ilchmann, A., Contributions to Time-Varying Linear Control Systems, (Thesis (1989), Verlag an der Lottbek: Verlag an der Lottbek Hamburg) · Zbl 0693.93048 [5] Ilchmann, A.; Owens, D. H.; Prätzel-Wolters, D., High gain robust adaptive controllers for multivariable systems, Systems Control Lett., 8, 397-404 (1987) · Zbl 0632.93046 [6] Logemann, H., Adaptive exponential stabilization for a class of nonlinear retarded processes, Math. Control Signals Systems (1990), to appear · Zbl 0714.93038 [7] Mårtensson, B., Adaptive Stabilization, (Doctoral Dissertation (1986), Lund Institute of Technology) · Zbl 0651.93042 [8] Miller, D. E.; Davidson, E. J., An adaptive controller which provides Lyapunov stability, IEEE Trans. Autom. Control, 34, 6, 599-609 (1989) · Zbl 0689.93040 [9] Nussbaum, R. D., Some remarks on a conjecture in parameter adaptive control, Systems Control Lett., 3, 243-246 (1983) · Zbl 0524.93037 [10] Owens, D. H.; Chotai, A.; Abiri, A., Parametrization and approximation methods in feedback theory with applications in high-gain, fast-sampling, and cheap-optimal control, IMA J. Math. Control. Inform., 1, 147-171 (1984) · Zbl 0668.93063 [11] Owens, D. H.; Prätzel-Wolters, D.; Ilchmann, A., Positive-real structure and high-gain adaptive stabilization, IMA J. Math. Control Inform., 4, 167-181 (1984) · Zbl 0631.93058 [12] Prätzel-Wolters, D.; Owens, D. H.; Ilchmann, A., Robust stabilization by high gain feedback and switching, Internat. J. Control, 49, 1861-1868 (1989) · Zbl 0683.93061 [13] Willems, J. C.; Byrnes, C. J., Global adaptive stabilization in the absence of information on the sign of the high frequency gain, (Lect. Notes in Control and Information Science No. 62 (1984), Springer-Verlag: Springer-Verlag Berlin), 49-57 · Zbl 0549.93043 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.