An Iterative Technique to Stabilize a Linear Time Invariant Multivariable System with Output Feedback.
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION HAMPTON VA LANGLEY RESEARCH CENTER
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The problem of finding a physically realizable, i.e. constant gain, output-feedback controller which will stabilize an unstable plant is one of the oldest and most fundamental problems in control theory. In spite of its long history, this problem still remains unsolved even in the seemingly simple case of linear plants. In this paper, an iterative procedure for determining the constant gain matrix that will stabilize a linear constant multivariable system using output feedback is described. The use of this procedure avoids the transformation of variables which is required in other procedures. For the case in which the product of the output and input vector dimensions is greater than the number of states of the plant, we are able to give a rather general solution. In the case in which the states exceed the product of input and output vector dimensions we are able to present a least square solution which may not be stable in all cases. The results are illustrated with examples.
- Numerical Mathematics