| The admissibility for positive discrete-time singular systems and stability prop-erty for positive discrete-time switched singular systems are discussed in this paper.In Chapter1, we state the backgrounds and the current development of the problem. In Chapter2, the admissibility of positive discrete-time singular systems are discussed. Firstly, according to the lyapunov inequality, which is a condition of stability for the positive discrete-time singular system, a necessary and sufficient condition for the system to be admissible is given in term of linear matrix inequali-ties. Furthermore, when the system has a monomial decomposition, a necessary and sufficient condition for admissibility is established by means of generalised lyapunov equation and rank. Finally, a numerical example is given to illustrate the validi-ty of the proposed conditions. In Chapter3, we consider stability of the positive switched singular system under arbitrary switching. Firstly, assume the positive switched singular system has a consistent initial condition and a image, It is proved that the stability of positive standard switched system implies positive switched singular system is stable by using an auxiliary standard positive switched system, two sufficient conditions for stability under arbitrary switching are explored. Fur-thermore, when the system has a monomial decomposition, a necessary condition for stability is established by means of matrix decomposition. Finally, a numerical example is given to illustrate the validity of the proposed conditions. |
