Abstract
This paper concerns with the balancing theory for the system governed by diffusion partial differential equation, which is refereed here as infinite dimensional system or distributed-parameter system. Based on the eigenvalue-eigenfunction structure of Laplacian differential operator, the approximate controllability and initial observability are constructed. In order to perform the balanced realization for infinite dimensional system, a brief review on finite dimensional balancing is presented, and more intuitive meaning of balanced realization is then obtained. After defining the Hankel operator of the infinite dimensional system, we compute the Hankel singular value and construct the energy balancing. And then, the model reduction problem is discussed. In the sequel, numerical simulation of the balanced model reduction for one-dimensional heat equation is conducted.
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