Stability of reset switching systems

In the design of switching control systems, the analysis of transient signals is of utmost importance. Each time a control transfer takes place, the resulting transient response may degrade performance. When switching takes place rapidly, interaction between switching transients may cause instability even when each of the ‘component’ loops are stable taken separately. We examine the issues of controller realization and controller initialization in the context of switching systems. Our objective is to minimize the performance degradation caused by transient signals at controller transitions, while guaranteeing stability under arbitrary switching. Some theoretical tools are needed to analyze such systems, where the states are permitted to change discontinuously at mode switches. We consider a general Lyapunov function approach to analyze the stability of ‘reset switching systems’, and use it to devise some LMI methods for synthesizing stabilizing reset schemes.