Preservation of dissipativity under multirate sampling with application to nonlinear H∞ control

This paper deals with a common practical problem where the output of a nonlinear sampled-data system is constrained to be measured at a relatively lower sampling rate. Designing a continuous-time controller that satisfies a specific dissipation inequality, the dissipativity of the digitally implementation of the emulated controller in a multirate control scheme is analyzed. It is shown that the closed-loop multirate system preserves similar dissipation inequality for the state feedback law in a semiglobal practical sense. Moreover, we propose a unified framework for designing nonlinear multirate sampled-data control systems in presence of disturbance inputs via emulation method and the multirate nonlinear H
_∞
control is addressed as a special application. Simulation results validate that the H
_∞
performance criterion is achieved not only with a preferable behavior but also under much lower measurement sampling rate, in comparison with the fast single-rate setup.