The Study Of Robust Stabilization For Uncertain Positive Systems

The uncertainties of system matrices and constraints on states are widely existed in practical systems, leading to declining the system performance or even destroying stabilities, and also making difficulties for the stability analysis of systems and the controllers design. On the other hand, most of the materials exist in the form of non-negative variables in the word. Therefore, researching on the dynamical properties of positive systems with non-negative state variables, especially on the robust stabilization and constraints on states in uncertain systems, have important realistic significance. This paper studies the problems of two kinds of uncertain continuous positive systems, whose inputs and states are bounded, the thesis concerns are as follows:A robust stabilization method is proposed for the problem of a class of uncertain continuous positive systems, whose inputs and states are bounded. First, by using the properties of Metzler matrices, a necessary and sufficient condition is established, which guarantees that the systems are positive and the states are bounded. Based on the stability theories of positive systems, another necessary and sufficient condition is given to ensure the asymptotical stabilities of the systems. Under the bounds on inputs and states, the robust states feedback controller is designed in terms of linear programming methods. Finally, simulation examples illustrate the effectiveness of the proposed algorithm.A robust stabilization method is proposed for a class of uncertain continuous interconnected systems. First of all, by using matrix transformation, the interconnected system is transformed into a general continuous system to be analyzed, which is equivalent to the interconnected system. A method for the design of state feedback controller is established, which guarantees that the closed-loop interconnected system is positive and the states are asymptotically stable. Furthermore, based on the stability theories of robust stability, another necessary and sufficient condition is given to ensure that uncertain interconnected systems are positive and the states are asymptotically stable, at the same time, a robust stabilization method is proposed for the closed-loop systems. Finally, simulation examples illustrate the effectiveness of the proposed algorithm.