Resilient Static Output Feedback Robust H_∞Control For Positive Systems

Positive systems are encountered in almost all fields, for instance, eco-nomics, engineering, ecology, social science and so on. In recent years, positive systems have attracted much attention of control theorists and obtained a lot of excellent results. However, many well-established results for general linear systems may not be applied to positive systems because of the fact that positive systems are defined on cones rather than on linear spaces. This feature also makes the control synthesis problems for positive systems more challenging.First of all, research of positive systems is introduced and the related the-ories of which are given briefly. Then the research background of this paper is given and the significance of research is indicated. Based on linear matrix inequality(LMI) and bounded real lemma in this paper, in terms of the cone complementarity linearization techniques, problems of resilient static output feedback robust H∞control are discussed for cases of continuous positive sys-tems and discrete positive systems.In Chapter2, resilient static output feedback robust H∞control for con-tinuous positive systems is investigated. Firstly, by means of a small scalar, a sufficient condition of resilient static output feedback robust H∞control for continuous positive systems is obtained via linear matrix inequality and bounded real lemma, which is more useful for the design of resilient static output feedback controller because the controller parameter is separated from the unknown parameter. Then, based on the above condition, an inference for the special case of the control matrix is given and a sufficient condition of resilient static output feedback robust H∞control for more general continu-ous positive systems is established. Furthermore, the desired controller gain matrix can be derived via the cone complementarity linearization techniques directly. Finally, a numerical simulation to show the validity of the results is provided.In Chapter3, resilient static output feedback robust H∞control for dis-crete positive systems is discussed. A sufficient condition of resilient static output feedback robust H∞control for discrete positive systems and an infer-ence are obtained via a similar method. Then a sufficient condition of resilient static output feedback robust H∞control for more general discrete positive systems is given. The controller can also be obtained via the cone complemen-tarity linearization techniques. Finally, a numerical simulation is presented to show the validity of the results.