Asymptotic stability of nonlinear control systems described by difference equations with multiple delays

Electronic Journal of Differential Equations

Volumn 2000, Issue , 2000, Pages

  Niamsup, P ^a,b   Phat, V N ^a,b  

^a University Hospital Chiangmai   (Thailand)

^b INSTITUTE OF MATHEMATICS   (Viet Nam)

Author keywords

Difference equations; Gronwall inequality; Holder condition; Multiple delay; Nonlinear control systems; Stability

Indexed keywords

EID: 52849088461     PISSN: 10726691     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. R.P Agarwal, Difference Equations and Inequalities. Marcel Dekker, New York, 1992.
2. N.S. Bay and V.N. Phat. On the stability of nonlinear nonstationary discretetime systems. Vietnam J. of Math., 4(1999), 311-319.
3. R. Gabasov., F. Kirillova, V. Krakhotko and S. Miniuk. Controllability theory of linear discrete-time systems. Diff. Equations, 8(1972), 767-773, 1081-1091, 1282-1291 (in Russian).
4. X. Huimin and L. Yongqing. The stability of linear time-varying discrete system with time-delay. J. Math. Anal. Appl., 188(1994), 66-77.
5. V.S. Kozyakin, A. Bhaya and E. Kaszkurewicz. A global asymptotic stability result for a class of discrete nonlinear systems. Math. Contr. Sig. Systems, 12(1999), 143-166.
6. J.P. LaSalle. The Stability and Control of Discrete Processes. Springer-Verlage, New York, 1986.
7. V. Lakshmikantham, S. Leela and A. Martyniuk. Stability Analysis of Nonlinea Systems. Marcel Dekker, New York, 1989.
8. A.D. Martinyuk. Lectures on Qualitative Theory of Difference Equations. Nauk Dumka, Kiev, 1972 (in Russian).
9. R. Naulin and C.J. Vanegas, Instability of discrete systems. Electron. J. of Diff. Eqns., 1998(1998), No.33, 1-11.
10. V.N. Phat. Constrained Control Problems of Discrete Processes. World Scientific, Singapore, 1996.
11. V.N. Phat. Weak asymptotic stabilizability of discrete-time systems given b set-valued operators. J. Math. Anal. Appl., 202(1996), 363-378.
12. V.N. Phat. On the stability of time-varying systems. Optimization, 45(1999), 237-254.
13. V.N. Phat. Controllability of linear discrete-time systems with multiple delay on controls and states. Int. J. of Control, 5(1989), 1645-1654.
14. J. Popenda, On the systems of discrete inequalities of Gronwall type. J. Math. Anal. Appl., 183(1994), 663-669.
15. E.D. Sontag. Mathematical Control Theory. Springer-Verlag, New York, 1990.
16. T. Taniguchi. On the estimate of solutions of perturbed nonlinear difference equations. J. Math. Anal. Appl., 149(1994), 599-610.
17. X. Yang and Y. Stepanenko. A stability criterion for discrete nonlinear systems with time delayed feedback. IEEE Trans, on AC, 39(1994), 585-588.