研究期間：10108~10207;A positive system is a dynamic system whose state variables are confined to be nonnegative for all times. Positive systems appear in various fields, e.g., biomedicine, pharmacokinetics, ecology, chemical engineering, and industrial engineering, etc. Since the parameter perturbations or uncertainties are inevitable in a physical system, in this two-year project, we will investigate the positivity and stability of linear uncertain systems. In the first year, continuous-time linear uncertain systems will be considered. First, new necessary and sufficient conditions will be derived for the positivity and stability assurance of linear systems with interval uncertainty. Then, new robustness conditions will be provided for systems with conic uncertainty. In the second year, we will focus on the robustness analysis and design of the positivity and stability of discrete-time linear uncertain systems. As in the continuous-time case, new necessary and sufficient criteria for ensuring the positivity and stability of discrete-time interval systems will be derived firstly. Then the conic uncertainty will be considered and new criteria will be proposed. It is mentioned that the uncertainty in conic form is more general than those in interval and polytopic forms. In addition, unlike some in the literature, the criteria to be proposed in this 2-year project do not impose any pre-restrictions on the open-loop system matrices and input matrices. This will further increase the applicability of the proposed criteria.
