Event-Triggered Filter Design of Positive Systems With State Saturation

• Published in: IEEE systems journal Vol. 15; no. 3; pp. 4281 - 4292
• Main Authors: Zhang, Junfeng, Raissi, Tarek, Shao, Yu, Cai, Xiushan
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additives; Automatic; Automation; Engineering Sciences; Error analysis; Event-triggered filter; Filter design (mathematics); Liapunov functions; linear copositive Lyapunov function; Linear programming; Loss measurement; Lower bounds; Lyapunov methods; positive systems; Saturation; Stability criteria; state saturation; Symmetric matrices; Upper bounds
• ISSN: 1932-8184; 1937-9234; 1937-9234; 1932-8184
• DOI: 10.1109/JSYST.2020.3019489

This article deals with event-triggered filter design of positive systems subject to state saturation. An event-triggering condition in the form of 1-norm is established based on the error and the measurable output. Under the presented event-triggering condition, the filter systems are transformed into interval uncertain systems. The positivity of the filter and error dynamics is achieved by considering the lower bound of the interval systems. Using a linear copositive Lyapunov function, the stability is guaranteed by considering the upper bound of the interval systems. By virtue of linear programming, an <inline-formula><tex-math notation="LaTeX">\ell _1</tex-math></inline-formula>-gain filter is designed for the systems subject to exogenous disturbance. Then, multiplicative and additive gain fluctuations are introduced. Two classes of nonfragile filters are proposed, and a cone is constructed to guarantee that the states of the systems with state saturation can keep inside it. Finally, two examples are given to illustrate the effectiveness of the proposed approach.