|Autors: Perev, K. L.|
Title: Gramians computation for parabolic distributed parameter systems
Keywords: reachabiity gramian, observability gramian, distributed parameter system
Abstract: The paper considers the problem of gramians computation for linear parabolic distributed parameters systems like the heat flow in a rod. The solution of the described partial differential equation is derived by applying the approach of time-space separation and by using the spectral method. By analogy to the finite dimensional case, it is shown that the derived solution consists of two parts. The first part is due to the initial conditions and participates in forming the observability gramian of the system. The second part is due to the system input and takes part in computing the reachability gramian. Different cases for problem definition in terms of different boundary conditions are given, showing how in such cases, the presented method can be used for gramians computation.
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