On state and output stabilization of discrete delay systems

• Autorzy: Karrakchou J. , Namir A. , Lahmidi F. , Daafi B.
• Języki publikacji: EN

Abstrakty

EN

The problem of the state and output stabilization of discrete-time delay systems on Hilbert spaces is considered. Sufficient and necessary conditions for the state stabilization are given. Analogue results for the output stabilization are presented. This work is organized in three sections. The state stabilization problem is examined in section 2. The three principle notions of stability and stabilizability (uniform, strong and weak) are investigated. Using the state space technique, it is shown that this problem can be tackled considering an equivalent non delayed system. Sufficient and necessary conditions for the stabilization of the new system are then established. Using these results and similar methods, sufficient and necessary conditions for the output stabilization are developed in section 3. To illustrate this work, some examples are given.

Słowa kluczowe

EN

discrete-time system; delay systems; stability; state stabilization; output stabilization

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2004
• Tom: Vol. 14, no. 3/4
• Strony: 287--298
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Karrakchou J.

• LERMA, EGT, Ecole Mohammadia d'ingénieurs, Maroc

autor

Namir A.

• Faculté des Sciences Ben M'Sik, Maroc

autor

Lahmidi F.

• Faculté des Sciences Ben M'Sik, Maroc

autor

Daafi B.

• Faculté des Sciences Ben M'Sik, Maroc

Bibliografia

• [1] L. Baghdadi: Stabilisation des systèmes linéaires dans les espaces de Hilbert. Thèse de Magister, Département de Mathématiques, Université d’Oran, 1985.
• [2] A. V. Balakrishnan: Strong stabilizability and the steady state Riccati equation. Applied Mathematics and Optimization, 7 (1981), 335-345.
• [3] S. P. Banks: State-space and frequency-domain methods in the control of distributed parameter systems. Peter Peregrinus, London, 1983.
• [4] C. D. Benchimol: Feedback stabilizability in Hilbert spaces. J. of Applied Mathematics and Optimization, 4 (1978), 225-248.
• [5] R. F. Curtain and H. J. Zwart: An introduction to infinite-dimensional linear systems theory. Springer-Verlag, New York, 1995.
• [6] F. Huang: Strong asymptotic stability of linear dynamical systems in Banach spaces. J. of Differential Equations, 104 (1993), 307-324.
• [7] H. Logemann: Stability and stabilizability of linear infinite-dimensional discretetime systems. IMA Journal of Mathematical Control and Information, 9 (1992), 255-263.
• [8] F. Lahmidi, A. Namir, M. Rachik and J. Karrakchou: Stabilizability and compensator design for discrete-time delay systems in Hilbert spaces. International J. of Systems Science, 30(3), (1999), 331-342.
• [9] R. Rabah and D. Ionescu: Stabilization problem in Hilbert spaces. International J. of Control, 46(6), (1987), 2035-2042.
• [10] J. M. Schumacher: Dynamic feedback in finite and infinite-dimensional linear systems. Mathematical Center Tracts No. 143, Mathematical Centrum, Amsterdam. 1981.