Sampling Dependent Stability Results for Aperiodic Sampled-Data Systems
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Sampling Dependent Stability Results for Aperiodic Sampled-Data Systems∗ SHAO Hanyong · YUAN Guangxia
DOI: 10.1007/s11424-020-9057-4 Received: 20 February 2019 / Revised: 26 October 2019 c The Editorial Office of JSSC & Springer-Verlag GmbH Germany 2020 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 Lyapunovlike 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. Keywords tems.
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Asymptotic stability, Lyapunov-like functional, polytopic uncertainties, sampled-data sys-
Introduction
Sampled-data systems have received substantial attention over the last two decades due to their wide applications in digital control systems and networked control systems[1–7] . As a basic property, the stability for sampled-data systems has been an interesting topic, which can be divided into two classes: Stability analysis under arbitrary sampling with bounded sampling interval[8] , and stabilization by designing sampling sequences. For the latter, the stabilization via event-triggered scheme is an emerging area; in this regard, we refer readers to [9, 10], among others. In [9] distributed event-triggered control for networked control systems with stochastic cyber-attacks was considered. In [10] state estimation for cyber-physical systems with limited SHAO Hanyong (Corresponding author) · YUAN Guangxia The Institute of Automation, Qufu Normal University, Rizhao 276826, China. Email: [email protected]; Yuan [email protected]. ∗ 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 HANYONG · YUAN GUANGXIA
communication resources was investigated, where an event-triggered scheme was introduced to relieve the effects brought by limited communication resources. For the former, see [11, 12] for example. Stability results were obtained in [11] for sampled-data systems with quantization and actuator saturation, while in [12] synchronization was studied via stability a
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