Exponential ISS properties for impulsive interconnected systems

This paper investigates the problem of exponential input-to-state stability (e-ISS) for impulsive interconnected systems. A new concept input-to-state exponent property (IS-E) including input-to-state positive exponent property (IS-E⁺), input-to-state zero exponent property (IS-E⁰) and input-to-state negative exponent property (IS-E^-), is proposed for dynamical systems with external input. By using IS-E estimations of subsystems, multiple Lyapunov functions method and average dwell time condition, the e-ISS criteria for continuous-time/discrete-time impulsive interconnected systems are established respectively. The ISS small-gain condition required in the literature for interconnected systems is relaxed if every subsystem has e-ISS property.