## Rocky Mountain Journal of Mathematics

### On the Improvement of Linear Discrete System Stability: The Maximal Set of the $F$-Admissible Initial States

#### Article information

Source
Rocky Mountain J. Math., Volume 34, Number 3 (2004), 1103-1120.

Dates
First available in Project Euclid: 5 June 2007

https://projecteuclid.org/euclid.rmjm/1181069845

Digital Object Identifier
doi:10.1216/rmjm/1181069845

Mathematical Reviews number (MathSciNet)
MR2087449

Zentralblatt MATH identifier
1066.93046

#### Citation

Rachik, M.; Lhous, M.; Tridane, A. On the Improvement of Linear Discrete System Stability: The Maximal Set of the $F$-Admissible Initial States. Rocky Mountain J. Math. 34 (2004), no. 3, 1103--1120. doi:10.1216/rmjm/1181069845. https://projecteuclid.org/euclid.rmjm/1181069845

#### References

• L. Baghdadi, Stabilisation des systèmes linéaires dans les espaces de Hilbert, Thèse de Magister, Département de Mathématiques, Université d'Oran, 1985.
• A.V. Balakrishnan, Applied functional analysis, Springer-Verlag, Berlin, 1976.
• S. P. Banks, State-space and frequency-domain methods in the control of distributed parameter systems, Peter Peregrinus, London, 1983.
• A. Benzaouia, The regulator problem for a class of linear systems with constrained control, Systems Control Lett. 10 (1988), 357-363.
• G. Bitsoris, On the positive invariance of polyhedral sets for discrete-time systems, Systems Control Lett. 11 (1988), 243-248.
• R.F. Curtain and A.J. Pritchard, Infinite dimensional linear systems theory, Springer-Verlag, Berlin, 1978.
• E.G. Gilbert and Tin Tan, Linear systems with state and control constraints: The theory and application of maximal output admissible sets, IEEE Trans. Automat. Contr. 36 (1991), 1008-1019.
• P.O. Gutman and M. Cwikel, An algorithm to find maximal state constraint sets for discrete-time linear dynamical systems with bounded controls and states, IEEE Trans. Automat. Contr. AC-30, 251-254.
• P.O. Gutman and P. Hagander, A new design of constrained controllers for linear systems, IEEE Trans. Automat. Contr. AC-30 (1985), 22-33.
• C.D. Johnson and W.M. Wonham, On a problem of Letov in optimal control, Trans. ASME J. Basic Engrg. Ser. D 87 (1965), 81-89.
• S.S. Keerthi, Optimal feedback control of discrete-time systems with state-control constrains and general cost functions, Ph.D. Dissertation, Computer Informat. Control Engrg., University of Michigan, Ann Arbor, Michigan, 1986.
• S.S. Keerthi and E.G. Gilbert, Optimal infinite horizon feedback laws for a general class of constrained discrete-time systems: Stability and moving-horizon approximations, J. Optim. Theory Appl. 57 (1988), 265-293.
• A.J. Pritchard and J. Zabczyk, Stability and stabilizability of infinite dimensional systems, SIAM Rev. 23 (1981), 25-52.
• R. Rabah and D. Ionescu, Stabilization problem in Hilbert spaces, Internat. J. Control 46 (1987), 2035-2042.
• M. Rachik, A. Abdelhak and J. Karrakchou, Discrete systems with delays in state, control and observation: The maximal output sets with state and control constraints, Optimization 42 (1997), 169-183.
• M. Rachik, E. Labriji, A. Abkari and J. Bouyaghroumni, Infected discrete linear systems: On the admissible sources, Optimization 48 (2000), 271-289.
• M. Rachik, M. Lhous, A. Tridane and A. Abdelhak, Discrete nonlinear systems: On the admissible nonlinear disturbances, J. Franklin Inst. 338 (2001), 631-650.
• M. Rachik, A. Tridane and M. Lhous, Discrete infected controlled nonlinear systems: On the admissible perturbation, SAMS 41 (2001), 305-323.
• J.M. Schumacher, A direct approach to compensator design for distributed parameter systems, SIAM J. Control Optim. 21 (1983), 823-836.
• R. Triggiani, On the stabilizability problem in Banach spaces, J. Math. Anal. Appl. 52 (1975), 383-403.
• M. Vassilaki, J.C. Hennet and G. Bistoris, Feedback control of linear discrete time systems under state and control constrains, Internat. J. Control 47 (1988), 1727-1735.
• V.I. Vorotnokov, Partial stability and control, Birkhauser, Boston, 1998.
• W.M. Wonham, Linear multivariable control, A geometric approach, Springer-Verlag, New York, 1985.
• K. Yosida, Functional analysis, Springer-Verlag, New York, 1980.
• K. Yoshida, Y. Nishimura and Y. Yonezawa, Variable gain feedback control for linear sampled-data systems with bounded control, Control Theory Adv. Tech. 2-2 (1986), 313-323.
• K. Yoshida, H. Kawabe, Y. Nishimura and Y. Yonezawa, A design of saturating control systems with state and input constrains, Proc. 12th IFAC World Congress (Sydney), Vol. 1, 1993, pp. 81-86.