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The problem of constructing a canonical representation for an arbitrary continuous piecewise-linear (PWL) function in any dimension is considered in this paper. We solve the problem based on a general lattice PWL representation, which can be determined for a given continuous PWL function using existing methods. We first transform the lattice PWL representation into the difference of two convex functions, then propose a constructive procedure to rewrite the latter as a canonical representation that consists of at most η-level nestings of absolute-value functions in n dimensions, hence give a thorough solution to the problem mentioned above. In addition, we point out that there exist notable differences between a lattice representation and the two novel general constructive representations proposed in this paper, and explain that these differences make all the three representations be of their particular interests. [ABSTRACT FROM AUTHOR]

In this note, the authors propose a generalization of the well known Wiener-Hopf design method of optimal controllers and filters, applicable to a certain class of systems described by fractional order differential equations, the so called rational order systems that, in the Laplace domain, are described by transfer functions which are quotients of polynomials in sα, α = (1 / q), q being a positive integer. As can be verified in the literature, such transfer functions arise in the characterization of some industrial processes and physical systems which can be adequately modeled using fractional calculus, or when modeling some distributed parameter systems by finite dimensional models. A brief exposition of the standard Wiener-Hopf method, and some fundamental considerations about rational order systems are given before presenting the proposed procedure. Illustrative examples are discussed. [ABSTRACT FROM AUTHOR]