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 continuous-time 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 a full reset system, 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 discrete-time reset systems and give an appropriate definition of the reset system in order to preserve the (Q,S,R)−(Q,S,R)−dissipativity of the base linear system under reset actions. As a result, ℓ2ℓ2-stability of feedback interconnected dissipative control reset systems is obtained.