A passivity based approach to predefined-time stabilization

Passivity theory is an efficacious framework in designing control laws, in particular, predefined-time stabilizing control laws. To that end, this paper discusses a predefined-time variant of passivity, associated Lyapunov tools, and basic analysis of this property through feedback interconnection. In particular, a series of predefined-time passivity definitions are discussed which allow to establish a relationship between the passivity framework and predefined-time stability. These definitions are exploited for designing control laws that render a passive system predefined-time stable about an equilibrium point. Moreover, several negative feedback interconnections of these systems are discussed to investigate the predefined-time passivity properties and predefined-time stability of an equilibrium point (when external inputs are zero). The efficacy of the proposed results is illustrated through academic and realistic examples, and comparison is also done with other existing methods.