Towards ℓ2ℓ2-stability of discrete-time reset control systems via dissipativity theory

This paper proposes conditions on input-output stability of discrete-time reset systems by using some key dissipativity properties. In the continuoustime setting, dissipativity of the base linear system is preserved under reset actions if the storage function is decreasing at reset times. Indeed, when the reset system is full reset, the dissipativity of the base linear system ensures the dissipativity of the reset system. However, in the discrete-time setting, this condition on the storage function is not enough to ensure the dissipativity of the base linear system. We define some dissipativity properties of discretetime reset systems and give an appropriate definition of the reset system in order to preserve the (Q, S,R)−dissipativity of the base linear system under reset actions. As a result, l2-stability of feedback interconnected dissipative control reset systems is obtained.