Hessenberg and Hessenberg/triangular forms in linear system thcory†

In this paper we distinguish between free Hessenberg forms, where only the system matrix is transformed into a special structure, and system Hessenberg forms, where either an input or output matrix is simultaneously simplified. We show how the freedom in the choice of the transformation matrix for the free Hessenberg form can be used to obtain a unique system Hessenberg form. We discuss numerical aspects and outline some basic applications for both types of Hessenberg forms in control and system theory. We show that the system Hessenberg form can be extremely sensitive to perturbations, a property not necessarily shared by the free Hessenberg form. Several examples are explored, and a first-order perturbation analysis is given. Analogous aspects are also discussed for the Hessenberg/triangular forms resulting from reduction of a matrix pencil. The main emphasis of this paper is on systems with one input.     

Estimation of Radiation Incident on Bifacial Albedo-Collecting Panels

In this paper we present a method to predict the radiation incident on both front and back faces of a bifacial photovoltaic panel surrounded by several diffusely reflecting surfaces. The incident irradiance on the panel is obtained from a mathematical model that considers both the effect of the interreflections between the reflector surfaces and the effect of the collector shadow. The model was validated experimentally for several albedo reflector configurations. The results of applying this model to several configurations of reflector planes using data for Madrid are presented. It is shown that in some cases an increasement in annual radiation incident on bifacial photovoltaic panels of nearly 70% can be achieved when compared to the radiation incident on conventional monofacial panels.