×

Robust stability for sampled-data control systems. (English) Zbl 0684.93052

Summary: We consider the robust stability of a continuous-time system under computer control. The uncertainty is modeled as additive perturbations to the matrices in a continuous-time state space description of the plant. Our methods exploit the resulting exponential-like uncertainty structure is the sampled-data control system and we develop sufficient conditions for such a system to be robustly stable.

MSC:

93C57 Sampled-data control/observation systems
93B35 Sensitivity (robustness)
93D20 Asymptotic stability in control theory
93C05 Linear systems in control theory
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Åstrom, K. J.; Wittenmark, B., Computer Controlled Systems, Theory and Design (1984), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0217.57903
[2] Bernstein, D. S., Robust static and dynamic output-feedback stabilization: deterministic and stochastic perspectives, IEEE Trans. Automat. Control, 32, 12, 1076-1084 (1987) · Zbl 0632.93056
[3] Bernstein, D. S.; Haddad, W. M., Robust stability and performance analysis for state space systems via quadratic Lyapunov bounds, (Proc. IEEE Conf. Decision and Control. Proc. IEEE Conf. Decision and Control, Austin, TX (1988)) · Zbl 0701.93077
[4] Brewer, J. W., Kronecker products and matrix calculus in system theory, IEEE Trans. Circuits and Systems, 25, 9, 772-781 (1978) · Zbl 0397.93009
[5] Corless, M., Stabilization of uncertain linear systems, (Proc. IFAC Workshop on Model Error Concepts and Compensation. Proc. IFAC Workshop on Model Error Concepts and Compensation, Boston, MA (1985)) · Zbl 0682.93040
[6] Hollot, C. V.; Arabacioglu, M., \(l\) th-step Lyapunov min-max controllers: Stabilizing discrete-time systems under real parameter variations, (Proc. American Control Conference. Proc. American Control Conference, Minneapolis, MN (1987)), 496-501
[7] Magana, M. E.; Zak, S., Robust state feedback stabilization of discrete-time uncertain dynamical systems, IEEE Trans. Automat. Control, 33, 9, 887-891 (1988) · Zbl 0663.93054
[8] Manela, J., Deterministic Control of Uncertain Linear Discrete and Sampled-Data Systems, (Ph.D. Dissertation (1985), Univ. Calif: Univ. Calif Berkeley, CA)
[9] Naylor, A. W.; Sell, G. R., Linear Operator Theory in Engineering and Science (1971), Holt, Rinehart and Winston: Holt, Rinehart and Winston New York
[10] Soroka, E.; Shaked, U., On the robustness of LQ regulators, IEEE Trans. Automat. Control, 29, 7, 664-665 (1984) · Zbl 0541.93016
[11] Thompson, P. M.; Dailey, R. L.; Doyle, J. C., New conic sectors for sampled-data feedback systems, Systems Control Lett., 7, 395-404 (1986)
[12] Tiedemann, A. R.; De Koning, W. L., The equivalent discrete-time optimal control problem for continuous-time systems with stochastic parameters, Internat. J. Control, 40, 3, 449-466 (1984) · Zbl 0551.93080
[13] Van Loan, C. F., Computing integrals involving the matrix exponential, IEEE Trans. Automat. Control, 23, 3, 395-404 (1978) · Zbl 0387.65013
[14] Varadarajan, V. S., Lie Groups, Lie Algebras, and Their Representations (1984), Springer-Verlag: Springer-Verlag New York · Zbl 0955.22500
[15] Wilson, D. A., Convolution and Hankel operator norms for linear systems, IEEE Trans. Automat. Control, 34, 1, 94-97 (1988) · Zbl 0661.93022
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.