On the use of backward Euler for sampled-data control design

ALEXIS VALLARELLA; HERNÁN HAIMOVICH; PAULA CARDONE

Virtual

Congreso; 27º Congreso de Control Automático AADECA 2020; 2020

Asociación Argentina de Control Automático (AADECA)

Several control design strategies for sampled-datasystems are based on a discrete-time model. In general, the exactdiscrete-time model of a nonlinear system is difficult or impossibleto obtain, and hence approximate discrete-time models may beemployed. Existing results provide conditions under which thestability of an approximate discrete-time model in closed-loopensures the practical stability of the corresponding (unknown)exact discrete-time model, ?practical? meaning that trajectoriesof the closed-loop system are ensured to converge to a boundedregion whose size can be made as small as desired by limiting themaximum sampling period. In recent works, we have shown thatnot only practical but also a type of asymptotic stability can beensured, provided a novel model consistency condition, namedRobust Equilibrium-Preserving Consistency (REPC), is satisfied.We have also proved that explicit Runge-Kutta models satisfy theREPC condition and hence control design ensuring asymptoticstability can be performed by means of such approximate models.In this context, the contribution of the current paper consists inshowing that the Backward Euler model, which is an implicitRunge-Kutta model, also satisfies the REPC property and couldbe used for control design, as well.