On the calculation of time-varying stability radii

International Journal of Robust and Nonlinear Control

Volumn 8, Issue 12, 1998, Pages 1043-1058

  Wirth, Fabian ^a  

^a UNIVERSITY OF BREMEN   (Germany)

Author keywords

Average yield; Discount rates; Discrete inclusions; Generalized spectral radius; Lyapunov exponents; Optimal control; Real stability radius

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; LYAPUNOV METHODS; OPTIMAL CONTROL SYSTEMS; STABILITY;

GENERALIZED SPECTRAL RADIUS; STABILITY RADIUS;

SYSTEM STABILITY;

EID: 0032183095     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1239(1998100)8:12<1043::AID-RNC364>3.0.CO;2-H     Document Type: Article

References (31)

1. Hinrichsen, D. and A. J. Pritchard, 'Stability radii of linear systems', Systems Control Lett., 7, 1-10 (1986).
2. Hinrichsen, D. and A. J. Pritchard, 'Stability radius for structured perturbations and the algebraic Riccati equation', Systems Control Lett., 8, 105-113 (1986).
3. Hinrichsen, D. and A. J. Pritchard, 'Real and complex stability radii: a survey', in Control of Uncertain Systems, D. Hinrichsen and B. Mårtensson (Eds), Progress in System and Control Theory, Vol. 6, Birkhäuser, Basel, 1990, pp. 119-162.
4. Qiu, L., B. Bernhardsson, A. Rantzer, E. J. Davison, P. M. Young and J. C. Doyle, 'A formula for computation of the real stability radius', Automatica, 31, 879-890 (1995).
5. Sreedhar, J., P. Van Dooren and A. L. Tits, 'A level-set idea to compute the real Hurwitz-stability radius', in Proc. 34th Conf. on Decision and Control New Orleans, LA, December 1995, pp. 126-127.
6. Hinrichsen, D. and A. J. Pritchard, 'Destabilization by output feedback', Differential Integr. Equations, 5, 357-386 (1992).
7. Berger, M. A. and Y. Wang, 'Bounded semigroups of matrices', Linear Algebra Appl., 166, 21-27 (1992).
8. Gurvits, L., 'Stability of discrete linear inclusions', Linear Algebra Appl., 231, 47-85 (1995).
9. Lagarias, J. C. and Y. Wang, 'The finiteness conjecture for the generalized spectral radius of a set of matrices', Linear Algebra Appl., 214, 17-42 (1995).
10. Wirth, F., 'Dynamics of time-varying discrete-time linear systems: spectral theory and the projected system', SIAM J. Control Optim., 36(2), (1998), to appear.
11. Barabanov, N. E., 'Lyapunov indicator of discrete inclusions. I', Automat. Remote Control, 49(2), 152-157 (1988).
12. Barabanov, N. E., 'Lyapunov indicator of discrete inclusions. II', Automat. Remote Control, 49(3), 283-287 (1988).
13. Barabanov, N. E., 'Lyapunov indicator of discrete inclusions. III', Automat. Remote Control, 49(5), 558-565 (1988).
14. Barabanov, N. E., 'Method for the computation of the Lyapunov exponent of a differential inclusion', Automat. Remote Control, 50(4), 475-479 (1989).
15. Gripenberg, G., 'Computing the joint spectral radius', Linear Algebra Appl., 234, 43-60 (1996).
16. Maesumi, M., 'An efficent lower bound for the generalized spectral radius of a set of matrices', Linear Algebra Appl., 240, 1-7 (1996).
17. Wirth, F., 'Convergence of the value functions of discounted infinite horizon optimal control problems with low discount rates', Math. Oper. Res., 18(4), 1006-1019 (1993).
18. Wirth, F., 'Asymptotics of value functions of discrete-time discounted optimal control', Report 411, Institut für Dynamische Systeme, Universität Bremen, 1997.
19. Grüne, L., 'Numerical stabilization of bilinear control systems', SIAM J. Control Optim., 34(6), 2024-2050 (1996).
20. Colonius, F. and W. Kliemann, 'The Lyapunov spectrum of families of time varying matrices', Trans. Am. Math. Soc., 348, 4389-4408 (1996).
21. Colonius, F. and W. Kliemann, 'Stability radii and Lyapunov exponents', in Proc. Workshop Control of Uncertain Systems, D. Hinrichsen and B. Mårtensson (Eds), Bremen 1989, Progress in System and Control Theory, Vol. 6, Birkhäuser, Basel, 1990, pp. 19-55.
22. Colonius, F. and W. Kliemann, 'Maximal and minimal Lyapunov exponents of bilinear control systems', J. Differential Equations, 101, 232-275 (1993).
23. Hinrichsen, D., A. Ilchmann and A. J. Pritchard, 'Robustness of stability of time-varying linear systems', J. Differential Equations, 82(2), 219-250 (1989).
24. Wirth, F. and D. Hinrichsen, 'On stability radii of infinite dimensional time-varying discrete-time systems', IMA J. Math. Control Inform., 11, 253-276 (1994).
25. Hinrichsen, D. and N. K. Son, 'Stability radii of positive discrete-time systems', Report 329, Institut für Dynamische Systeme, Universität Bremen, 1994.
26. Daleckii, J. L. and M. G. Krein, Stability of Solutions of Differential Equations in Banach Spaces, Translations of Mathematical Monographs, Vol. 43, AMS Providence, RI, 1974.
27. Przyluski, K. M., 'Remarks on the stability of linear infinite-dimensional discrete-time systems', J. Differential Equations, 72(2), 189-200 (1988).
28. Bertsekas, D., Dynamic Programming Deterministic and Stochastic Models, Prentice-Hall, Englewood Cliffs, NJ, 1987.
29. Dolcetta, I. C. and H. Ishii, 'Approximate solutions of the Bellman equation of deterministic control theory', Appl. Math. Optim., 11, 161-181 (1984).
30. Falcone, M., 'A numerical approach to the infinite horizon problem of deterministic control theory', Appl. Math. Optim., 15, 1-13 (1987). Corrigenda, ibid., 23, 213-214 (1991).
31. Grüne, L., 'An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation', Numer. Math., 75, 319-337 (1997).