Positive Observers And Output-Feedback Stabilization For Interval Positive Systems With Delays

Positive systems are dynamic systems which abound in almost all fields, for instance, engineering, ecology, economics, biomedicine, social science and so on. A common property of positive systems is that the states and outputs are nonnegative whenever the initial conditions and inputs are nonnegative. Since the states of positive systems are confined within a "cone" located in the positive orthant rather than in linear spaces, many well-established results for general linear systems can not be readily applied to positive systems. This feature makes the analysis and synthesis of positive systems an important job.In this thesis, the problem of positive observers design and output-feedback stabilization is studied for positive linear time-delay systems with interval un-certainties. The necessary and sufficient conditions or sufficient conditions for the existence of positive observers and output-feedback controllers and the de-sign methods are presented. Numerical examples are also given to illustrate the effectiveness of the proposed results. This thesis contains the following three chapters.In Chapter1, the background of positive time-delay systems are reviewed, and some advances in the study of positive observers for positive time-delay systems are recalled. Some open problems in this field are pointed out as well. Finally, the notations used in this thesis is listed.In Chapter2, the positive observers and output-feedback stabilization are investigated for continuous-time interval positive systems with delays. For sys-tems without external input, necessary and sufficient conditions or sufficient conditions for the existence of positive observers, which guarantee that the augmented observing systems are asymptotically stable or exponentially sta-ble, are presented in terms of linear matrix inequalities (LMIs). For systems with external input, necessary and sufficient conditions or sufficient conditions for the existence of observer-based output-feedback controllers, which guar-antee that the closed-loop systems are asymptotically stable or exponentially stable, are given in terms of LMIs together with a matrix equality constraint. The desired controller gain matrices can be solved effectively via the cone complementarity linearization techniques.Chapter3is devoted to the problem of positive observers and output-feedback stabilization for discrete-time interval positive systems with delays. The positive observers and output-feedback controllers are designed for discrete-time positive time-delay systems with existence conditions and detailed design methods being proposed.