Abstract
This paper investigates sampling dependent stability for aperiodic sampled-data systems by employing a Lyapunov-like functional that is time-dependent, and not imposed to be definite positive. Based on the system information on the sampling interval wholly rather than partly, a new Lyapunov-like functional is constructed, which extends existing ones by introducing the integral of the system state and the cross terms among this integral and the sampled state. To take advantage of the integral of the system state, integral equations of the sampled-data system are explored when estimating the derivative of the extended functional. By the Lyapunov-like functional theory, a new sampling dependent stability result is obtained for sampled-data systems without uncertainties. Then, the stability result is applied to sampled-data systems with polytopic uncertainties and a robust stability result is derived. At last, numerical examples are given to illustrate that the stability results improve over some existing ones.
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This paper was supported by the Natural Science Foundation of China under Grant No. 61374090, the Program for Scientific Research Innovation Team in Colleges and Universities of Shandong Province, and the Taishan Scholarship Project of Shandong Province.
This paper was recommended for publication by Editor SUN Jian.
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Shao, H., Yuan, G. Sampling Dependent Stability Results for Aperiodic Sampled-Data Systems. J Syst Sci Complex 34, 588–601 (2021). https://doi.org/10.1007/s11424-020-9057-4
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DOI: https://doi.org/10.1007/s11424-020-9057-4