Asymptotic stability for sampled-data systems under nonuniform sampling with sampling period dependent controls

ALEXIS VALLARELLA; HERNAN HAIMOVICH

San Juan

Congreso; XIX Reunión de Trabajo en Procesamiento de la Información y Control, RPIC'2021; 2021

One difficult aspect of control design for nonlinear sampled-data systems from a discrete-time standpoint is how to establish stability properties when the true or exact discrete-time model is unknown or cannot be analytically computed. Existing results can ensure stability of the nonlinear sampled-data system at the sampling instants based on three ingredients: (a) an approximate discrete-time model for the open-loop system, (b) the stability of the approximate model in closed loop with some control law, and (c) a bound on the mismatch between the approximate and exact models, a bound that can be obtained without having to compute the exact model. The current contribution is to complement existing Input-to-State Stability (ISS) results that provide a bound on the state evolution at the sampling instants by showing that an ISS-type bound is also valid at all times and not just at the sampling instants, even under nonuniform sampling and when the control law may be sampling-period dependent. We present an example of sampling period-dependent control synthesis based on (approximate) Runge-Kutta models. We derive controllers of increasing complexity that outperform an emulated continuous-time control law, possibly allowing the use of larger sampling periods while preserving stability.