Systems engineering for very large systems

Very large integrated systems have always posed special problems for engineers. Whether they are power generation systems, computer networks or space vehicles, whenever there are multiple interfaces, complex technologies or just demanding customers, the challenges are unique. 'Systems engineering' has evolved as a discipline in order to meet these challenges by providing a structured, top-down design and development methodology for the engineer. This paper attempts to define the general class of problems requiring the complete systems engineering treatment and to show how systems engineering can be utilized to improve customer satisfaction and profit ability. Specifically, this work will focus on a design methodology for the largest of systems, not necessarily in terms of physical size, but in terms of complexity and interconnectivity

Realizations of infinite products, Ruelle operators and wavelet filters

Using the notions and tools from realization in the sense of systems theory, we establish an explicit and new realization formula for families of infinite products of rational matrix-functions of a single complex variable. Our realizations of these resulting infinite products have the following four features: 1) Our infinite product realizations are functions defined in an infinite-dimensional complex domain. 2) Starting with a realization of a single rational matrix-function $M$, we show that a resulting infinite product realization obtained from $M$ takes the form of an (infinite-dimensional) Toeplitz operator with a symbol that is a reflection of the initial realization for $M$. 3) Starting with a subclass of rational matrix functions, including scalar-valued corresponding to low-pass wavelet filters, we obtain the corresponding infinite products that realize the Fourier transforms of generators of $\mathbf L_2(\mathbb R)$ wavelets. 4) We use both the realizations for $M$ and the corresponding infinite product to produce a matrix representation of the Ruelle-transfer operators used in wavelet theory. By matrix representation we refer to the slanted (and sparse) matrix which realizes the Ruelle-transfer operator under consideration.Comment: corrected versio