Null controllability of a nonlinear system with variable time delay

Controlabilidad de ecuaciones diferenciales retardadas semilineales impulsivas con retardo infinito y condiciones no locales.

“…There are many concepts of controllability depending on whether the control variable has restrictions, such as local controllability, which has been strongly studied by Chukwu (1979Chukwu ( , 1980Chukwu ( , 1987Chukwu ( , 1991Chukwu ( , 1992, Mirza & Womack (1972), Sinha &Yokomoto (1980), andSinha (1985).…”

A Constructive Method of Solving Local Boundary Value Problems for Nonlinear Systems with Perturbations and Control Delays

“…The study of BVPs over finite time intervals for such types of systems includes finding necessary and sufficient conditions of complete, local, constrained, relative, or approximate controllability for linear [14][15][16][17][18][19][20][21][22], bilinear [23], semilinear [24][25][26], and nonlinear [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] systems of differential equations; studying and estimating the attainability domain (see [20,46,47]); and developing methods to construct controls under which the trajectory connects the given points in the phase space (see [20,45]). For linear stationary systems, there exist criteria of complete controllability in terms of the matrices of the right-hand side, which take into account a time delay in control [14,15] or several delays in the system state [31].…”

“…In [24], the sufficient condition of controllability for semilinear system with lumped (also called discrete) and distributed delays in the state variables was given. References [27][28][29][30][32][33][34][36][37][38][39][40][41][42][43][44]46,48,49] considered the conditions of controllability, zero controllability, and relative and approximate controllability of nonlinear systems of ODEs with constant and variable delays taking into account control constraints and external perturbations.…”

Roughness of the Controllability for Time Varying Systems Under the Influence of Impulses, Delay, and Nonlocal Conditions

“…But, V. N. Do [14] weaker the conditions on f and prove the controllability of the system (1.1) ( without impulses, delay and non local conditions) containing Dauer's conditions; it is good to recall that all these conditions depends strongly on the linear system (1.6); especially, on the fundamental matrix Φ(t) of the linear system (2.9), which is in general not available in closed form. There are others concepts of controllability, perhaps, the local controllability, which has been studied by [4], [5], [6], [7], [8], [9], [28], [29], and [31], but as far as we know, without impulses and non local conditions. The controllability of di erential equation with impulses is in e ervescence now; for evolution equations there are papers by [30] by J.J. Nieto and C.C.…”