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We consider the problem of achieving prescribed-time stability (PT-S) in aclass of hybrid dynamical systems that incorporate switching nonlineardynamics, exogenous inputs, and resets. By "prescribed-time stability", werefer to the property of having the states converge to a particular compact setof interest before a given time defined a priori by the user. We focus ondynamical systems that achieve this property via time-varying gains. Forcontinuous-time systems, this approach has received significant attention inrecent years, with various applications in control, optimization, andestimation problems. However, its extensions beyond continuous-time systemshave been limited. This gap motivates this paper, which introduces a novelclass of switching conditions for switching systems with resets thatincorporate time-varying gains, ensuring the PT-S property even in the presenceof unstable modes. The analysis leverages tools from hybrid dynamical system'stheory, and a contraction-dilation property that is established for the hybridtime domains of the solutions of the system. We present the model and mainresults in a general framework and subsequently apply them to three novelapplications: (a) PT regulation of switching plants with no common Lyapunovfunctions; (b) PT control of dynamic plants with uncertainty and intermittentfeedback; and (c) PT decision-making in non-cooperative switching games viahybrid Nash seeking dynamics.

Prescribed-Time Control in Switching Systems with Resets: A Hybrid Dynamical Systems Approach