Relaxed Local Tracking Conditions for Markovian Jump Systems with Application to DC-DC Synchronous Buck Converters Under Load Resistance Switching Variations

This paper presents a local tracking control approach for DC–DC synchronous buck converters operating under randomly varying load resistance. The load variation is represented by a discrete-mode switching mechanism governed by a Markov stochastic process, allowing the converter dynamics to be modeled as a Markovian jump system. A mode-dependent state-feedback controller is developed based on linear matrix inequality (LMI)-based conditions that explicitly incorporate transition-rate information. By incorporating the transition characteristics into the controller design, the proposed method ensures stochastic local stability together with satisfactory tracking performance within a prescribed local stability region, while reducing the conservatism of conventional global-stability-based approaches. Simulation studies demonstrate that the proposed controller effectively regulates the converter under stochastic load variations.