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This work studies the null-controllability of a class of abstract parabolic
equations. The main contribution in the general case
consists in giving a short proof of an abstract version of a sufficient
condition for null-controllability which has been proposed by Lebeau and
Robbiano. We do not assume that the control operator is admissible.
Moreover, we give estimates of the control cost.
In the special case of the heat equation in rectangular domains, we provide
an alternative way to check...
This work studies the null-controllability of a class of abstract parabolic
equations. The main contribution in the general case
consists in giving a short proof of an abstract version of a sufficient
condition for null-controllability which has been proposed by Lebeau and
Robbiano. We do not assume that the control operator is admissible.
Moreover, we give estimates of the control cost.
In the special case of the heat equation in rectangular domains, we provide
an alternative way to check...
In this paper, the observability of fuzzy logic second order control system is studied from the aspect of fuzzy differential equations. The fuzzy observability in the weak sense is created using the concept of “likelihood” to indicate on which level and along which solution the state is most likely observable. One of the initial state range has been derived with the given input and output. The result generalizes the previous results.
Fast filtering algorithms arising from linear filtering and
estimation are nonlinear dynamical systems whose initial values
are the statistics of the observation process. In this paper, we
give a fairly complete description of the phase portrait for such
nonlinear dynamical systems, as well as a special type of naturally
related matrix Riccati equation.
We review the realization theory of polynomial (transfer function) matrices via "pure" generalized state space system models. The concept of an irreducible-at-infinity generalized state space realization of a polynomial matrix is defined and the mechanism of the "cancellations" of "decoupling zeros at infinity" is closely examined. The difference between the concepts of irreducibility and minimality of generalized state space realizations of polynomial (transfer function) matrices is pointed out...
This paper deals with the problem of tracking a reference signal while maintaining the stability of the closed loop system for linear time invariant systems with delays in the states. We show that conditions for the existence of a solution to this problem (the so-called regulation problem), similar to those known for the case of delay-free linear systems, may be given. We propose a solution for both the state and error feedback regulation.
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