Event-Triggered Functional Observer Design With $\epsilon$-Convergence for Interconnected Systems
Dinh Cong Huong, Van Thanh Huynh, Hieu Trinh
Abstract
This article considers the problem of designing robust event-triggered functional observers for linear interconnected systems with disturbances. The considered system comprises <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> interconnected subsystems where each subsystem is subject to unknown-but-bounded input disturbances that do not necessarily satisfy the observer matching condition. First, novel Zeno-free event-triggered mechanisms (ETMs) for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> subsystems of the considered interconnected system are proposed. Then, robust distributed functional observers are designed based on the proposed ETMs. The designed event-triggered functional observers are robust such that the observer error for each subsystem is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon _i$</tex-math></inline-formula> -convergent. This ensures that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$i$</tex-math></inline-formula> th estimated state vector of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$i$</tex-math></inline-formula> th subsystem converges robustly within an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon _i$</tex-math></inline-formula> -bound of the true state vector of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$i$</tex-math></inline-formula> th subsystem. Numerical examples are given to illustrate the effectiveness of the proposed design method.