Aperiodically Intermittent Control of Neutral Stochastic Delay Systems Based on Discrete Observations
研究了基于离散观测的中立随机时滞系统的非周期间歇控制问题，通过引入辅助系统方法，给出了观测周期上界和占空比下界，证明了系统在特定条件下指数稳定，并揭示了经典方法可能导致的误差累积现象。
In article, we study the problem of aperiodically intermittent control (APIC) for neutral stochastic delay systems (NSDSs) based on discrete observations. To overcome the difficulty caused by intermittent control, an auxiliary system is introduced. By using the Lyapunov function method, an upper bound of observation period <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\delta ^{*}$ </tex-math></inline-formula> is obtained. If observation period <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\delta < \delta ^{*}$ </tex-math></inline-formula> , then the auxiliary system is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> th <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(p\geq 2)$ </tex-math></inline-formula> -moment exponentially stable. In addition to the fixed observation period <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\delta < \delta ^{*}$ </tex-math></inline-formula> , this article gives a method to design an aperiodically intermittent controller and obtains a lower bound of duty cycle for all fixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0 < \underline {T}\leq \overline {T}$ </tex-math></inline-formula> with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\underline {T}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\overline {T}$ </tex-math></inline-formula> being lower bound and upper bound of control frames. That is, we proved the NSDSs with the intermittent discrete observation controller is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> th <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(p\geq 2)$ </tex-math></inline-formula> -moment exponentially stable if the auxiliary system is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> th <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(p\geq 2)$ </tex-math></inline-formula> -moment exponentially stable. We call this method the auxiliary system method (ASM). In fact, different from mainstream techniques, the ASM used in this article can handle the case of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0 < \underline {T}\leq \overline {T} < \delta $ </tex-math></inline-formula> even if <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\delta $ </tex-math></inline-formula> is small enough. Besides, this article reveals one interesting phenomenon: classic methods may lead to error accumulation, which cannot be avoided in APIC or periodically intermittent control (PIC) for NSDSs. Finally, one numerical example, one application, and one comparison are given to show the usefulness and correctness of the proposed results.