Stability analysis and stabilization synthesis of asynchronously sampled-data systems via integral looped functionals composed of bivariate functions

This paper proposes a novel looped-functional approach that provides tractable conditions for the stability analysis and stabilization synthesis of linear systems under asynchronously sampled inputs. To reduce the conservatism of these conditions, a general looped-functional framework is introduced that includes existing approaches as special cases, and thereby yields more relaxed conditions expressed as linear matrix inequalities. Compared to several existing works, the proposed approach offers not only a general but also a specific functional structure composed of bivariate functions. One of these variables is associated with differentiation, and the other is associated with integration. The proposed framework provides relaxed conditions for both the Lyapunov functional and its time derivative, which play essential roles in the conservatism reduction of the conditions for stability analysis and stabilization synthesis. Seven numerical examples demonstrate the effectiveness of the proposed approach through maximum admissible sampling intervals, with only a small additional number of decision variables.