(Integral)ISS of Switched and Time-Varying Impulsive Systems Based on Global State Weak Linearization

It is shown that impulsive systems of nonlinear, time-varying, and/or switched form that allow a stable global state weak linearization are jointly input-to-state stable (ISS) under small inputs and integral ISS. The system is said to allow a global state weak linearization if its flow and jump equations can be written as a (time-varying, switched) linear part plus a (nonlinear) perturbation satisfying a bound of affine form on the state. This bound reduces to a linear form under zero input but does not force the system to be linear under zero input. The given results generalize and extend previously existing ones in many directions: 1) no (dwell-time or other) constraints are placed on the impulse time sequence; 2) the system needs not be linear under zero input; 3) existence of a (common) Lyapunov function is not required; and 4) the perturbation bound needs not be linear on the input.