Abstract
Abstract This paper considers the nonfragile observer-based guaranteed cost finite-time control of discrete-time positive impulsive switched systems(DPISS). Firstly, the positive observer and nonfragile positive observer are designed to estimate the actual state of the underlying systems, respectively. Secondly, by using the average dwell time(ADT) approach and multiple linear co-positive Lyapunov function (MLCLF), two guaranteed cost finite-time controller are designed and sufficient conditions are obtained to guarantee the corresponding closed-loop systems are guaranteed cost finite-time stability(GCFTS). Such conditions can be solved by linear programming. Finally, a numerical example is provided to show the effectiveness of the proposed method.
Highlights
The switched system is a type of hybrid systems
This paper considers the nonfragile observer-based guaranteed cost nite-time control of discretetime positive impulsive switched systems(DPISS)
By using the average dwell time(ADT) approach and multiple linear co-positive Lyapunov function (MLCLF), two guaranteed cost nite-time controller are designed and su cient conditions are obtained to guarantee the corresponding closed-loop systems are guaranteed cost nite-time stability(GCFTS). Such conditions can be solved by linear programming
Summary
The switched system is a type of hybrid systems It comprises a set of a di erential or di erence equations and a switched controller, which designate the switching between subsystems at a speci c interval of time. It has been studied very well, see [1,2,3,4]. In [12], the exponential stability for a class of discrete-time positive impulsive switched linear systems was studied. In [13], the nitetime stability for a class of discrete-time positive impulsive switched time-delay systems under asynchronous switching was discussed. [12] and [13] are based on the assumption of the known state
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