Switching Rule Design with Chattering Reduction

Abstract This paper presents a continuous-time switching control strategy tailored to mitigate chattering in switched affine systems under digital implementation. Inspired by discrete-time practical stability concepts, the proposed method introduces an optimized geometric relaxation framework that restructures the state-space geometry around the equilibrium point. Specifically, the control law optimizes the volume of an invariant ellipsoidal attractor while systematically relaxing the stability constraints along non-critical directions, thereby allowing bounded, controlled limit cycles to manifest without triggering high-frequency switching. The switching rule and the robust invariant set boundaries are simultaneously synthesized via a set of linear matrix inequalities (LMIs). The methodology is validated through two numerical benchmarks: a DC machine speed control and a DC–DC buck converter under parametric uncertainties. Simulation results at 100 kHz demonstrate a significant reduction in the effective switching frequency—achieving 143.6 Hz for the DC machine and 1.19 kHz for the buck converter—while strictly maintaining bounded tracking errors. These findings demonstrate that the proposed technique can successfully reduce the chattering condition in switched systems, increasing performance and broadening the practical applicability of switched control systems.