Consecutive time-intervals-dependent looped functionals for stability analysis of linear systems with asynchronous sampling

Abstract

The purpose of this article is to propose a novel framework employing a looped-functional approach for the stability analysis of continuous-time linear systems with asynchronous sampling. In this approach, a negative forward-difference of a Lyapunov functional consisting of a Lyapunov function and a looped-functional sufficiently guarantees asymptotic stability of the sampled-data systems. To reduce the conservatism of the stability criteria, we develop a consecutive time-intervals-dependent looped-functional approach that satisfies a convex looping inequality with respect to each sampling interval. Compared to the existing looped-functional approaches, the proposed method provides a more general looped-functional and in turn a more relaxed stability conditions. The existing looped functionals and their associated looping conditions can be considered as special cases of the proposed ones. This relationship can easily be verified by excluding time-intervals-dependent terms in the general looped functional. Four numerical examples that consider both periodic and asynchronous sampling cases demonstrate that the proposed looped-functional approach shows better performance in terms of allowable maximum sampling intervals at a cost of a small additional number of decision variables.