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With the significant trend towards variable frequency in heating ventilating and air-conditioner (HVAC) loads, the inverter-based air conditioner load (IACL) clusters are poised to become the mainstay in participating in demand response (DR). During the process of DR, once the indoor temperature exceeds the comfort constraint, HVAC load must be forced to exit DR, which brings correlation to the behaviour of the preceding and following periods, making cluster optimization modelling and solution difficult. In order to solve the problems, this paper proposes an analogue ON/OFF state-switching (AOSS) control method suitable for IACL cluster participating in DR. Firstly, the critical working point corresponding to the comfort constraint is analysed for eliminating the temporal coupling for IACL. Then, an AOSS control method is proposed based on the critical point analysis. The feasibility of the proposed AOSS control is validated by the experimental results, with the Hisense KFR-75W/T08SBp-A2 inverter-based air conditioning DR experimental platform. Furthermore, by using the proposed AOSS control, a day-ahead scheduling model is constructed, and, the traditional state-queuing (SQ) model is transplanted to the IACL cluster for short-term power control. And the case studies verified the effectiveness and applicability of the day-ahead scheduling model and the transplanted SQ model. • Analysing the critical working point corresponding to the comfort constraint. • AOSS control is proposed to eliminate the temporal coupling for IACL. • Aggregation and optimal dispatching for IACL cluster in day-ahead time scale. • Ultra-short time scale IACL cluster power control. [ABSTRACT FROM AUTHOR]