Amato, Francesco; Ariola, Marco; Dorato, Peter Finite-time control of linear systems subject to parametric uncertainties and disturbances. (English) Zbl 0983.93060 Automatica 37, No. 9, 1459-1463 (2001). The authors consider a linear system subject to time-varying parametric uncertainties and to exogenous constant disturbances \[ \dot x(t) = A(p)x(t) + B(p)u(t) + G(p)w, \] where \(A(p)\in\mathbb R^{n\times n}\), \(B(p)\in\mathbb R^{n\times m}\) and \(G(p)\in\mathbb R^{n\times l}\). The concept of finite-time boundedness for the state of a system, when not only given initial conditions but also external constant disturbances are considered, is introduced. The main result provided is a sufficient condition guaranteeing finite-time boundedness via state feedback. It can be applied to problems with both non-zero initial conditions and unknown constant disturbances. This condition is turned into an optimization problem involving LMIs. A detailed example is presented to illustrate the proposed methodology. Reviewer: Alexandr B.Vasil’ev (Odessa) Cited in 247 Documents MSC: 93D21 Adaptive or robust stabilization 93C73 Perturbations in control/observation systems 15A39 Linear inequalities of matrices Keywords:uncertain linear systems; parametric uncertainties; state feedback finite-time stability; finite-time boundedness; disturbance-rejection Software:LMI toolbox PDF BibTeX XML Cite \textit{F. Amato} et al., Automatica 37, No. 9, 1459--1463 (2001; Zbl 0983.93060) Full Text: DOI References: [1] Amato, F.; Garofalo, F.; Glielmo, L.; Pironti, A., Robust and quadratic stability via polytopic set covering, International Journal of Robust and Nonlinear Control, 5, 745-756 (1995) · Zbl 0851.93058 [2] Bhattacharyya, S. P.; Chapellat, H.; Keel, L. H., Robust control: The parametric approach (1995), Prentice Hall PTR: Prentice Hall PTR Upper Saddle River, NJ · Zbl 0838.93008 [3] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory (1994), SIAM Press: SIAM Press Philadelphia, PA · Zbl 0816.93004 [4] Corless, M., Robust stability analysis and controller design with quadratic Lyapunov Functions, (Zinober, A. S.I., Variable structure and lyapunov control (1993), Springer: Springer Berlin) · Zbl 0803.93032 [6] Gahinet, P.; Nemirovski, A.; Laub, A. J.; Chilali, M., LMI control toolbox (1995), The Mathworks Inc: The Mathworks Inc Natick, MA [7] Garofalo, F.; Celentano, G.; Glielmo, L., Stability robustness of interval matrices via quadratic Lyapunov forms, IEEE Transactions on Automatic Control, 38, 281-284 (1993) · Zbl 0774.93061 [9] Geromel, J. C.; Peres, P. L.D.; Bernussou, J., On a convex parameter space method for linear control design of uncertain systems, SIAM Journal on Control and Optimization, 29, 381-402 (1991) · Zbl 0741.93020 [11] Grantham, W. J., Estimating Reachable Sets, ASME Journal of Dynamic Systems and Measurement Control, 103, 420-422 (1981) · Zbl 0467.93032 [12] 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 [13] Zhou, K.; Doyle, J. C., Essentials of Robust Control (1998), Prentice Hall, Inc: Prentice Hall, Inc 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.