An optimal algorithm for testing positive realness of discrete-time descriptor systems is established in this note. The input for this algorithm is state space representation. It is derived new sufficient and necessary conditions on positive realness by using the simple algebraic transformations. Based on this theorem, optimization model can be established. The algorithm for testing positive realness of discrete-time descriptor systems is easier and more efficient. Numerical tractability of the results is illustrated by two examples. These analysis results also may have applications in controller design for discrete-time descriptor systems.
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