Quadratic dissipation inequalities for nonlinear systems using event-triggered controllers

We present a method to design event-triggered controllers that ensure the satisfaction of quadratic dissipation inequalities for nonlinear sampled-data systems. We follow an emulation approach for this purpose. We first assume that a static feedback law is designed in continuous-time to guarantee such a dissipativity property. We then take into account sampling and we synthesize a triggering rule to preserve dissipativity. The parameters of the sampling law can be adjusted to approximately recover the quadratic terms of the initial supply rate with any desired accuracy by solving a linear matrix inequality, which can always be satisfied. We then tailor our results to specific quadratic dissipativity properties, namely (strict-)passivity and L₂-stability. Our results cover periodic sampling as a particular case, for which we provide new explicit bounds on the maximum allowable sampling period.