Research On Some Problems Of Positive Svstems

The positive systems refers to the state and output variables'constant non-negativity when the systems's initial state and control input are positive or non-negative. As the positive systems's state variable is limited to the positive quadrant.the analysis and control methods used in common systems are unable to be applied to the positive systems directly. In recent years, its dynamic property has drawn wide attention and achieved some valuable research results. LPV (Linear Parameter - Varying) systems is a coefficient matrix subject to the external parameters and measurable in any time. Through the analysis and design of parameters. LPV can be similar to the nonlinear systems. Therefore, the study of its dynamic property has become the hot issue in the control field. At present, the study concerning the positive LPV systems is still in an early stage. This paper will study on the integral control of positive systems as well as positive LPV systems as follows:(1) Study the design of positive system's static output feedback controller based on the finite frequency-domain. First, provide the necessary and sufficient conditions of closed-loop system being asymptotically stable and up to H? performance in the finite frequency-domain. On this basis, the static output feedback controller's necessary and sufficient conditions and detailed design will be achieved in a linear matrix inequality. Finally, the validity of the design method will be demonstrated by numerical example.(2) Study the design of LPV system's static output feedback controller. First, based on Lyapunov function as. well as slack variable introduction, the sufficient conditions of closed-loop system being asymptotically stable and positive will be provided. On this basis, the static-output feedback controller's integrated design will be achieved in a linear matrix inequality. At last, the validity of the design method will be demonstrated by numerical example.(3) Study the design of LPV system's observer. First, provide the sufficient conditions of the error svstem being asvmptoticallv stable and positive will be achieved in a linear matrix inequality. On this basis, the designing method of observe is established. At last, the validity of the design method will be demonstrated by numerical example.