Admissibility Analysis of Positive Discrete-time Descriptor System

The admissibility of positive discrete-time singular system is discussed in this paper, if a system is regular, causal, stable, we call it admissible. Firstly, according to the Lyapunov inequality*<0,which is a condition of stability for the positive discrete-time singular system, a necessary and sufficient condition for the system to be admissible are expressed in Linear Matrix Inequalities terms. Furthermore, suppose the system has a monomial decomposition, it is admissible if and only if there exists a positive definite diagonal matrix *, Finally, numerical example is given to illustrate the validity of the proposed conditions.(* Indicates a formula, please see the full text)