On the design of reset systems with unstable base: A fixed reset-time approach

Reset time-dependent systems are a sort of reset systems whose reset condition does not depend on particular states of the system but only on reset time intervals. This novel approach simplifies stability analysis that is generally guaranteed by checking the stability of an equivalent discrete system obtained by sampling the original system after every reset. Although stability analysis is simpler, it is well known that a reset time-dependent approach might deteriorate the resultant transient response if the reset intervals are chosen to be too large. Motivated by recent research on this field, this works contributes with a procedure to determine a sub-optimal reset interval for systems with unstable base system. Additionally, a criterion to determine whether the resultant transient response will be deteriorated is given. Both contributions rely on an analysis of the spectral radius of the transition matrix of the equivalent discrete system. Extensive simulations are given to support the validity and effectiveness of our results.