Reset times-dependent stability of reset control with unstable base systems

Reset control systems are a special type of hybrid systems in which the time evolution depends both on continuous dynamics between resets and the discrete dynamics corresponding to the reset instants. In this work, stability of reset control systems is approached by using an equivalent (time-varying) discrete time system, and necessary and sufficient stability conditions that explicitly depends on the reset times are used. These conditions have been applied for the case in which the linear base control system is unstable.