ISSN:
1573-2878
Keywords:
Null-controllability with constraints
;
uniform asymptotic stability
;
controllability
;
complete linear systems
;
reachable sets
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Consider the following functional equations of neutral type: $$\begin{gathered} (i) (d/dt)D(t,x_t ) = L(t,x_t ), \hfill \\ (ii) (d/dt)D(t,x_t ) = L(t,x_t ) + B(t)u(t), \hfill \\ (iii) (d/dt)D(t,x_t ) = L(t,x_t ) + B(t)u(t) + f(t,x(t),u(t)), \hfill \\ \end{gathered} $$ whereD, L are bounded linear operators fromC([−h, 0],E n) intoE n for eachtɛ(σ, ∞) =J, B is ann ×m continuous matrix function,u:J →C m is square integrable with values in the unitm-dimensional cubeC m, andf(t, 0, 0)=0. We prove that, if the system (i) is uniformly asymptotically stable and if the controlled system (ii) is controllable, then the system (iii) is null-controllable with constraints, provided that $$f = f_1 + f_2 $$ , where $$\begin{gathered} |f_1 (t,\phi ,0)| \leqslant \varepsilon \parallel \phi \parallel , |f_2 (t,\phi ,0)| \leqslant \pi (t)\parallel \phi \parallel , t \geqslant \sigma , \hfill \\ \Pi = \int_0^\infty {\pi (t)dt〈 \infty .} \hfill \\ \end{gathered} $$
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00935324
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