Normal matrices and their stability properties: application to 2-D system stabilization

An approach is presented to 2-D system stabilization by constant state feedback that is based on assigning a closed-loop matrix that is two-dimensionally (2-D) similar to a stable normal matrix. First, it is shown that for normal matrices the sufficient Lyapunov stability condition is also necessary and that 1-D and 2-D BIBO stabilities are equivalent. Next, sufficient conditions or 2-D stabilization by constant state feedback are given where the closed-loop system matrix is 2-D similar to a normal matrix. Finally, the method is applied to two examples.<
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