An unknown linear plant will track an input command signal if the plant is driven by a controller whose transfer function approximates the inverse of the plant transfer function. An adaptive inverse identification process can be used to obtain a stable controller, even if the plant is nonminimum phase. A model-reference version of this idea allows system dynamics to closely approximate desired ...

We consider feed-forward neural networks with one non-linear hidden layer and linear output units. The transfer function in the hidden layer are either bell-shaped or sigmoid. In the bell-shaped case, we show how Bernstein polynomials on one hand and the theory of the heat equation on the other are relevant for understanding the properties of the corresponding networks. In particular, these tec...

We give a further elaboration of the fundamental connections between Lax-Phillips scattering, conservative input/state/output linear systems and Sz.-Nagy-Foias model theory for both the discreteand continuous-time settings. In particular, for the continuous-time setting, we show how to locate a scattering-conservative L2-well-posed linear system (in the sense of Staffans and Weiss) embedded in ...

Already since the beginning of infinite-dimensional systems theory, there has been interest in the state-space realization problem. The state-space realization problem is the problem of finding for a given function a system in state-space form whose transfer function equals the given function. If we start with a rational function, then it is well-known, that one can always find a system with fi...

In this paper, we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties. For the class of linear time-invariant dynamical systems, these characteristics are determined by transmission zeros of the inner factor of the system transfer function. The relation between nonminimum phase zeros and Hankel singular values of inner system...

A fault is (strongly) detectable if it is possible to construct a residual generator that is sensitive to the (constant) fault while decoupling all disturbances. Two new fault detectability criterions and three new strong fault detectability criterions are presented. For comparison, existing fault detectability criterions are reviewed. To prove the criterions, a framework of polynomial bases is...

Neural network has been applied in several classification problems such as in medical diagnosis, handwriting recognition, and product inspection, with a good classification performance. The performance of a neural network is characterized by the neural network’s structure, transfer function, and learning algorithm. However, a neural network classifier tends to be weak if it uses an inappropriat...

We study the optimal input-output stabilization of discrete time-invariant linear systems in Hilbert spaces by output injection. We show that a necessary and sufficient condition for this problem to be solvable is that the transfer function has a left factorization over H-infinity. Another equivalent condition is that the filter Riccati equation (of an arbitrary realization) has a solution (in ...

It has recently been shown that the identification of a linear time-invariant plant using closed-loop measurements with a known linear controller can be effectively tackled by regarding the unknown plant as a member of the set of all plants stabilized by the known linear controller. This set is parametrized by a Youla-Kucera parameter, itself a stable transfer function which, it turns out. can ...