Dissipative Control For Local Fractional Order Switched Systems

Fractional order switched systems are an important kind of hybrid systems.In recent years,there have been a lot of research results on the stability of such systems,but few studies on the dissipative properties of such systems.Most fractional order switched systems are based on Caputo fractional calculus theory.However,the definition of Caputo fractional order integral determines the limitation of this research,therefore,it is necessary to consider the theory and application of local fractional order calculus to study the dissipation control of local fractional order switched systems.In this paper,the finite time extended dissipation and exponential dissipation control of local fractional order switched systems are studied.Firstly,the research significance and development status of fractional order switched systems are introduced,at the same time,the research significance and current situation of local fractional order switched systems are introduced.Secondly,the finite time boundedness of local fractional order switched systems is analyzed.By means of linear matrix inequalities and mean resident time methods,the sufficient conditions for finite time augmented dissipation and exponential dissipation are obtained.Then,a state feedback controller and a non-fragile state feedback controller based on the full dimensional state observer are designed for the local fraction order switched systems.By selecting appropriate storage functions and using linear matrix inequalities,the sufficient conditions for asymptotic stability of the error system and finite time extended dissipation and exponential dissipation of the closed-loop system are obtained.At last,the main content of this paper is summarized.