Stability analysis of hybrid integrator-gain systems: A frequency-domain approach

• Published in: Automatica (Oxford) 2024-06, Vol.164, p.111641, Article 111641
• Main Authors: van den Eijnden, Sebastiaan, Heertjes, Marcel, Nijmeijer, Hendrik, Heemels, W.P.M.H. (Maurice)
• Format: Article
• Language: English
• Subjects: Frequency-domain; HIGS; KYP-lemma; Stability analysis
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2024.111641

The hybrid integrator-gain system (HIGS) has been introduced recently with the aim to overcome fundamental limitations of linear time-invariant (LTI) control systems. To support the analysis and design of HIGS-based controllers, in this paper a novel frequency-domain condition for stability analysis of the feedback interconnection of an LTI system and HIGS is presented. Compared to existing frequency-domain stability conditions such as the one extending the circle-criterion, the condition presented in this paper exploits explicit knowledge regarding HIGS’ switching strategy, thereby potentially providing a significantly less conservative condition. In particular, the novel condition in this paper guarantees the existence of a quadratic Lyapunov function that does not need to be positive definite within the full state space. The proposed condition can be verified graphically in a manner that is reminiscent of the classical Popov plot, as will be illustrated in an experimental case-study.