Base Vectors for Solving of Partial Differential Equations
نویسنده
چکیده
The distributed parameters systems can be described by linear two-dimensional (dependent on two spatial directions) parabolic partial differential equations. Using the finite difference method a distributed parameters system can be transformed to a linear discrete state space model. The controller design based on this description is complicated because of the large dimension of the model. Therefore, a model reduction method has to be used. We transform the state space model to the balanced realization of the system and show that the state vector of the model can be expressed as the series of columns of the transformation matrix. These columns can be imaged as base vectors of the state space.
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