Geodesic
Asymptotic stability of nonlinear control systems described by difference equations with multiple delays
Electronic journal of differential equations, Tome 2000 (2000)
In this paper we study nonlinear control systems with multiple delays on controls and states. To obtain asymptotic stability, we impose Holder-type assumptions on the perturbing function, and show a Gronwall-type inequality for difference equations with delay. We prove that a nonlinear control system can be stabilized if its linear control system can be stabilized. Some examples are included in the last part of this paper.
Classification : 93D20, 34K20, 49M70
Keywords: stability, difference equations, nonlinear control systems, Gronwall inequality, holder condition, multiple delay 
@article{EJDE_2000__2000__a210,
     author = {Niamsup,  P. and Vu Ngoc Phat},
     title = {Asymptotic stability of nonlinear control systems described by difference equations with multiple delays},
     journal = {Electronic journal of differential equations},
     year = {2000},
     volume = {2000},
     zbl = {0941.93052},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a210/}
}
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TI  - Asymptotic stability of nonlinear control systems described by difference equations with multiple delays
JO  - Electronic journal of differential equations
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%A Vu Ngoc Phat
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%J Electronic journal of differential equations
%D 2000
%V 2000
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%F EJDE_2000__2000__a210
Niamsup,  P.; Vu Ngoc Phat. Asymptotic stability of nonlinear control systems described by difference equations with multiple delays. Electronic journal of differential equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a210/