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

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