LMI-based stability analysis of linear hybrid systems with application to switched control of a refrigeration process

We consider continuous-time switched linear systems associated with linear state reset during mode switches, which are called linear hybrid systems and can be commonly found in switched control systems via bumpless transfer during controller switches. We use a multiple Lyapunov functions approach to develop constructive tools for stability analysis of linear hybrid systems. In particular, we derive a linear-matrix-inequalities based procedure to compute upper bounds of dwell time for uniform global exponential stability in linear hybrid systems, and we apply it to a refrigeration process that is regulated by several switched proportional-integral controllers via bumpless transfer.