Composite Anti-Disturbance Control of Hidden Semi-Markov Jump Systems via Disturbance Observer

• Published in: Journal of systems science and complexity Vol. 36; no. 6; pp. 2255 - 2273
• Main Authors: Men, Yunzhe, Sun, Jian
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2023; Springer Nature B.V
• Subjects: Complex Systems; Control; Control systems design; Controllers; Disturbance observers; H-infinity control; Liapunov functions; Linear matrix inequalities; Mathematical analysis; Mathematics; Mathematics and Statistics; Mathematics of Computing; Operations Research/Decision Theory; Stability analysis; Stability criteria; Statistics; Systems Theory; Composite control; hidden semi-Markov jump systems; disturbance observer; error
• ISSN: 1009-6124; 1559-7067
• DOI: 10.1007/s11424-023-2407-2

This paper focuses on the disturbance suppression issue of hidden semi-Markov jump systems leveraging composite control. The system consists of a semi-Markov layer and an observed mode sequence layer, and it is subject to a matched disturbance generated by an exogenous system and a mismatched disturbance that is norm bounded. The proposal is to design a composite controller based on a disturbance observer to counteract and attenuate the disturbances effectively. By constructing a special Lyapunov function comparison point, the exponential stability is analyzed with the stability criterion in the form of linear matrix inequality is established. Two simulation examples are provided to demonstrate the practical merits of the composite controller relative to the single H ∞ control.