Standard diffusive systems as well-posed linear systems
نویسنده
چکیده
In this paper we show that every diffusive system is a well-posed system in the sense of Salamon and Weiss. Furthermore, we characterize several systems theoretic properties of these systems, such as stability, controllability, and observability. Instead of referring to general results on well-posed linear system, we prove these results directly. Hence we hope that this paper will serve as a tutorial to well-posed linear systems.
منابع مشابه
Asymptotic Stability of Linear Conservative Systems When Coupled with Diffusive Systems
In this paper we study linear conservative systems of finite dimension coupled with an infinite dimensional system of diffusive type. Computing the time-derivative of an appropriate energy functional along the solutions helps us to prove the well-posedness of the system and a stability property. But in order to prove asymptotic stability we need to apply a sufficient spectral condition. We also...
متن کاملExplicit formulae for J−spectral factors for well-posed linear systems
The standard way to obtain explicit formulas for spectral factorization problems for rational transfer functions is to use a minimal realization and then obtain formulae in terms of the generators A, B, C and D. For well-posed linear systems with unbounded generators these formulae will not always be well-defined. Instead, we suggest another approach for the class of well-posed linear systems f...
متن کاملDiffusive systems coupled to an oscillator: a Hamiltonian formulation
The aim of this paper is to study a conservative wave equation coupled to a diffusion equation : this coupled system naturally arises in musical acoustics when viscous and thermal effects at the wall of the duct of a wind instrument are taken into account. The resulting equation, known as Webster-Lokshin model, has variable coefficients in space, and a fractional derivative in time. The port-Ha...
متن کاملTwo classes of passive time-varying well-posed linear systems
We investigate two classes of time-varying well-posed linear systems. Starting from a time-invariant scattering-passive system, each of the time-varying systems is constructed by introducing a time-dependent inner product on the state space and modifying some of the generating operators. These classes of linear systems are motivated by physical examples such as the electromagnetic field around ...
متن کاملClassical wavelet systems over finite fields
This article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. It is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008