179 research outputs found
Approximate controllability and lack of controllability to zero of the heat equation with memory
In this paper we consider the heat equation with memory in a bounded region
, , in the case that the propagation speed
of the signal is infinite (i.e. the Colemann-Gurtin model). The memory kernel
is of class . We examine its controllability properties both under the
action of boundary controls or when the controls are distributed in a subregion
of . We prove approximate controllability of the system and, in
contrast with this, we prove the existence of initial conditions which cannot
be steered to hit the target in a certain time , of course when the
memory kernel is not identically zero. In both the cases we derive our results
from well known properties of the heat equation
Prediction-Based Control of Linear Systems by Compensating Input-Dependent Input Delay of Integral-Type
International audienceThis study addresses the problem of delay compensation via a predictor-based output feedback for a class of linear systems subject to input delay which itself depends on the input. The equation defining the delay is implicit and involves past values of the input through an integral relation, the kernel of which is a polynomial function of the input. This modeling represents systems where transport phenomena take place at the inlet of a system involving a nonlinearity, which frequently occurs in the processing industry. The conditions of asymptotic stabilization require the magnitude of the feedback gain to comply with the initial conditions. Arguments for the proof of this novel result include general Halanay inequalities for delay differential equations and take advantage of recent advances in backstepping techniques for uncertain or varying delay systems
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