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Positive Descriptor Time-varying Discrete-time Linear Systems and Their Asymptotic Stability

Kaczorek T.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

2015

Vol. 9, no. 1

83--89

The positivity and asymptotic stability of the descriptor time-varying discrete-time linear systems are addressed. The Weierstrass-Kronecker theorem on the decomposition of the regular pencil is extended to the time-varying discrete-time descriptor linear systems. Using the extension necessary and sufficient conditions for the positivity of the systems are established. Sufficient conditions for asymptotic stability of the positive systems are presented. The effectiveness of the tests is demonstrated on the example.