Integral versions of input-to-state stability for dual-rate nonlinear sampled-data systems

TL;DR

This paper develops integral input-to-state stability concepts for dual-rate nonlinear sampled-data systems, using estimators to compensate for low measurement rates and establishing stability of both approximate and exact models.

Contribution

It introduces integral stability notions for dual-rate systems and shows controllers stabilize both approximate and exact models under low measurement conditions.

Findings

Controllers stabilize approximate models under low measurement rates.

Stability of exact models is achieved in dual-rate settings.

Numerical simulations confirm theoretical results.

Abstract

This paper presents versions of integral input-to-state stability and integral input-to-integral-state stability for nonlinear sampled-data systems, under the low measurement rate constraint. In particular, we compensate the lack of measurements using an estimator approximately reconstructing the current state. Interestingly, under certain checkable conditions, we establish that a controller that semiglobally practically integral input-to-(integral-) state stabilizes an approximate discrete-time model of a single-rate nonlinear sampled-data system, also stabilizes the exact discrete-time model of the nonlinear sampled-data system in the same sense implemented in a dual-rate setting. Numerical simulations are given to illustrate the effectiveness of our results.