Browsing by Subject "spectral methods"

Now showing 1 - 3 of 3

Access status: Open Access ,
The motion planning problem and exponential stabilization of a heavy chain. Part 2
(2008) Grabowski, Piotr
This is the second part of paper [P. Grabowski, <i>The motion planning problem and exponential stabilization of a heavy chain. Part I</i>, to appear in International Journal of Control], where a model of a heavy chain system with a punctual load (tip mass) in the form of a system of partial differential equations was interpreted as an abstract semigroup system and then analysed on a Hilbert state space. In particular, in [P. Grabowski, <i>The motion planning problem and exponential stabilization of a heavy chain. Part I</i>, to appear in International Journal of Control] we have formulated the problem of exponential stabilizability of a heavy chain in a given position. It was also shown that the exponential stability can be achieved by applying a stabilizer of the colocated-type. The proof used the method of Lyapunov functionals. In the present paper, we give other two proofs of the exponential stability, which provides an additional intrinsic insight into the exponential stabilizability mechanism. The first proof makes use of some spectral properties of the system. In the second proof, we employ some relationships between exponential stability and exact observability.
Access status: Open Access ,
Well-posedness and stability analysis of hybrid feedback systems using Shkalikov's theory
(2006) Grabowski, Piotr
The modern method of analysis of the distributed parameter systems relies on the transformation of the dynamical model to an abstract differential equation on an appropriately chosen Banach or, if possible, Hilbert space. A linear dynamical model in the form of a first order abstract differential equation is considered to be well-posed if its right-hand side generates a strongly continuous semigroup. Similarly, a dynamical model in the form of a second order abstract differential equation is well-posed if its right-hand side generates a strongly continuous cosine family of operators. Unfortunately, the presence of a feedback leads to serious complications or even excludes a direct verification of assumptions of the Hille-Phillips-Yosida and/or the Sova-Fattorini Theorems. The class of operators which are similar to a normal discrete operator on a Hilbert space describes a wide variety of linear operators. In the papers [12, 13] two groups of similarity criteria for a given hybrid closed-loop system operator are given. The criteria of the first group are based on some perturbation results, and of the second, on the application of Shkalikov's theory of the Sturm-Liouville eigenproblems with a spectral parameter in the boundary conditions. In the present paper we continue those investigations showing certain advanced applications of the Shkalikov's theory. The results are illustrated by feedback control systems examples governed by wave and beam equations with increasing degree of complexity of the boundary conditions.
Access status: Open Access ,
Zmiany widm w bliskiej podczerwieni (NIR) w poziomach organicznych pod drzewostanami bukowymi i świerkowymi
(Wydawnictwa AGH, 2006) Chodak, Marcin
Spectral methods utilizing different ranges of electromagnetic radiation may be applied to study soil organic matter quality. The objective of this study was to compare near infrared (NIR) spectra of organic layers under beech, spruce and mixed forest stands and to assign the observed spectral changes to chemical alterations of organic matter. Compared were second derivatives of the NIR spectra. The NIR spectra changed gradually in organic layers. The changes of intensities of the peaks, which may be assigned to certain chemical structures, reflected the changes in abundance of these structures and indicated differences among the studied stands resulting probably from different chemical composition of organic matter under different stands. The analysis of spectra indicated an increase of relative absorbance of the peaks at 2320 nm and 2360 nm within organic horizons, suggesting an increase of aliphatic compounds. On the contrary, the relative absorbance of the peaks at 1680 nm, 2140 nm and 2170 nm decreased within the organic horizons suggesting relative decrease of aromatic structures with depth. It was concluded that calibration of NIR spectra with standard chemical methods might enable application of NIR spectroscopy for quantitative assessment of chemical changes of soil organic matter during humification process.