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

ALEXIS VALLARELLA; PAULA CARDONE; HERNAN HAIMOVICH

Congreso; 27º Congreso Argentino de Control Automático AADECA?20 Virtual; 2020

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. The ?practical? nature of the propertymeans that trajectories of the closed-loop system are ensuredto converge to a bounded region whose size can be made assmall as desired by limiting the maximum sampling period.In recent works, we have shown that not only practical butalso a type of asymptotic stability can be ensured, provided anovel model consistency condition, named Robust Equilibrium-Preserving Consistency (REPC), is satisfied. We have also provedthat explicit Runge-Kutta models satisfy the REPC conditionand hence control design ensuring asymptotic stability can beperformed by means of such approximate models. In this context,the contribution of the current paper consists in showing thatthe Backward Euler model, which is an implicit Runge-Kuttamodel, also satisfies the REPC property and could be used forcontrol design, as well.