Stabilization of linear nonautonomous systems with norm-bounded controls

Journal of Optimization Theory and Applications

Volumn 131, Issue 1, 2006, Pages 135-149

  Phat, V N ^a   Niamsup, P ^b  

^a INSTITUTE OF MATHEMATICS   (Viet Nam)

^b CHIANG MAI UNIVERSITY   (Thailand)

Author keywords

Controllability; Lyapunov equations; Lyapunov functions; Nonautonomous systems; Riccati differential equations; Stabilizability

Indexed keywords

RICCATI EQUATIONS; STABILIZATION;

BOUNDED CONTROLS; LYAPUNOV EQUATION; LYAPUNOV'S FUNCTIONS; NON-AUTONOMOUS SYSTEM; RICCATI DIFFERENTIAL EQUATION; SIMPLE++; STABILIZABILITY; STABILIZABILITY CONDITIONS; STABILIZATION PROBLEMS;

LYAPUNOV FUNCTIONS;

EID: 33845636502     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-006-9129-1     Document Type: Article

References (19)

1. BOYD, S., EL GHAOUI, L., FERON, E., and BALAKRISHNAN, V., Linear Matrix Inequalities and Control Theory, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, Pennsylvania, Vol. 15, 1994.
2. CORLESS, M., and LEITMANN, G., Bounded Controllers for Robust Exponential Convergence, Journal of Optimization Theory and Applications, Vol. 76, pp. 1-12, 1993.
3. GIBSON, J. S., Riccati Equations and Numerical Approximations, SIAM Journal on Control and Optimization, Vol. 21, pp. 95-139, 1983.
4. NIAMSUP, P., and PHAT, V. N., Asymptotic Stability of Nonlinear Control Systems Described by Differential Equations with Multiple Delays, Electronic Journal of Differential Equations, Vol. 2000, pp. 1-17, 2000.
5. PHAT, V. N., Weak Asymptotic Stabilizability of Discrete Inclusions Given by Set-Valued Operators, Journal of Mathematical Analysis and Applications, Vol. 202, pp. 353-369, 1996.
6. PHAT, V. N., Stabilization of Linear Continuous Time-Varying Systems with State Delays and Norm-Bounded Uncertainties, Electronic Journal of Differential Equations, Vol. 2001, pp. 1-13, 2001.
7. BOUNIT, H., and HAMMOURI, H., Bounded Feedback Stabilization and Global Separation Principle of Distributed-Parameter Systems, IEEE Transactions on Automatic Control, Vol. 42, pp. 414-419, 1997.
8. SLEMROD, M., Feedback Stabilization of a Linear Control System in Hilbert Space with a priori Bounded Control, Mathematical Control and Signal Systems, Vol. 22, pp. 265-285, 1989.
9. SUN, Y. J., LIEN, H., and HSIED, J.G., Global Exponential Stabilization for a Class of Uncertain Nonlinear Systems with Control Constraints, IEEE Transactions on Automatic Control, Vol. 43, pp. 67-70, 1998.
10. SUSSMAN, H. J., SONTAG, E. D., and YANG, Y., A General Result on the Stabilization of Linear Systems Using Bounded Controls, IEEE Transactions on Automatic Control, Vol. 39, pp. 2411-2425, 1994.
11. SOLDATOS, A. G., and CORLESS, M., Stabilizing Uncertain Systems with Bounded Control, Dynamics and Control, Vol. 1, pp. 227-238, 1991.
12. SOLDATOS, A.G., CORLESS, M., and LEITMANN, G., Stabilizing Uncertain Systems with Bounded Control, Mechanics and Control, Los Angeles, California, pp. 415-428, 1990;
13. see also Lecture Notes in Control and Information Sciences, Springer, Berlin, Germany Vol. 151, 1991.
14. KALMAN, R., Contribution to the Theory of Optimal Control, Boletin de la Sociedad Matematica Mexicana, Vol. 5, pp. 102-119, 1960.
15. IKEDA, M., MAEDA, H., and KOMADA, S., Stabilization of Linear Systems, SIAM Journal on Control, Vol. 10, pp. 716-729, 1972.
16. MARSHALL, A. W., and OLKIN, L., Inequalities: Theory of Majorizations and Its Applications, Academic Press, New York, NY, 1979.
17. LAUB, A. J., Schur Techniques for Solving Riccati Equations, Feedback Control of Linear and Nonlinear Systems, Lecture Notes in Control and Information Sciences, Springer, Berlin, Germany, Vol. 39, pp. 165-174, 1982.
18. ABOU-KANDIL, H., FREILING, G., IONESCU, V., and JANK, G., Matrix Riccati Equations in Control and Systems Theory, Birkhauser, Basel, Switzerland, 2003.
19. THOMAS, W. R., Riccati Differential Equations, Academic Press, New York, NY, 1972.