Stability analysis of reset positive systems with discrete-time triggering conditions

This paper discusses the problem of stability analysis of reset positive systems based on discrete-time triggering conditions. A reset control system is positive, if for any nonnegative initial condition and input, its states and outputs are nonnegative whenever the reset actions occur. First, the relationship between reset positive systems (RPSs) with discrete-time triggering conditions and discrete-time switched positive systems (SPSs) is established, by which the stability problem of RPSs is transformed to that of SPSs. Then, some sufficient and necessary conditions of stability and tracking problem for RPSs are given.