stochastic robustness in switched systems: a novel control strategy for random time-iteration driven switching

This paper addresses the control of a category of continuous-time linear systems that switch between different modes, where the switching signals are driven by random time-iteration. the system under consideration is subject to uncertainties in the system dynamics and observation noise in the output measurements. we propose a robust control strategy that accounting for the random nature of the switching signals and the system uncertainties. the learning performance is examined using the lebesgue-p norm, leading to the derivation of a sufficient condition for convergence. the findings demonstrate that the proposed control law effectively addresses the tracking problem in switched systems, especially when the switching rules are expanded to the time-iteration domain using a stochastic framework, we introduce a groundbreaking control approach that guarantees the system's performance despite uncertainties and noise. through rigorous theoretical analysis, we prove the effectiveness of our suggested approach in achieving robust control and estimation performance.the results of this research contribute to the advancement of control theories and have potential applications in various fields, including power systems, robotics, and process control.