A hybrid index model for discrete-time reset control systems

This paper proposes a hybrid index model for discrete-time reset control systems. In this model, the system state is indexed by two indices. One represents the time steps, while the other records the number of resettings. Compared with the existing models for discrete-time reset control systems, the main benefit of the proposed model is that it inherits some of the key hybrid properties from its continuous-time counterpart. Based on this model, the concepts of hybrid solutions and forward completeness are defined. Then, for planar discrete-time reset systems, several conditions assuring forward completeness are obtained. In addition, boundedness of number of single-step resettings is also investigated for planar reset systems. Some examples are also provided to explain the proposed model and results.