Novel Equalities for Stability Analysis of Asynchronous Sampled-Data Systems

This paper is concerned with the stability analysis problems of asynchronous sampled-data systems with use of a input-delay approach, where a sampled-data system can be reformulated into a time-delay system having incremental delays. For these systems, this paper introduces a new looped-functional to utilize both integral states and their interval-normalized ones. Utilization of these two types of integral state variables in a construction of stability conditions has been effective in reducing the conservatism. Further, generalized equalities are proposed for the case utilizing these two types of integral states. The sampled-data system formulation consists of a sampled state, a system state and its derivative. Here, the sampled state between two consecutive sampling instants is a constant value and thus can be eliminated by an integration with Legendre polynomials of positive degrees. Consequently, the system formulation turns into the equalities consisting of state variables, sampled-state variables, integral state variables and their interval-normalized ones without additional slack matrices. Based on the proposed equalities, a large computational burden can be reduced while reducing the conservatism. The effectiveness of the proposed approaches is demonstrated via three numerical examples for the stability analysis of asynchronous sampled-data systems.