On semiglobal ISS under small inputs for discrete-time models of sampled-data systems

ALEXIS J. VALLARELLA; HERNÁN HAIMOVICH

Buenos Aires

Congreso; 2018 Argentine Conference on Automatic Control (AADECA); 2018

Asociación Argentina de Control Automático - AADECA

One control design approach for nonlinearcontinuous-time plants is known as Discrete-Time Design (DTD).This approach is usually based on approximate models given thatthe exact discrete-time model for a nonlinear plant is difficult orimpossible to obtain. In this context, there exist several resultsthat ensure robustness of the discrete-time models with respectto discrete-time disturbances (e.g. such as state-measurement oractuation errors). None of the existing conditions contemplate thecase in which the system achieves input-to-state stability whenthe inputs are smaller than a certain upper bound but maynot be defined or become unstable otherwise. We aim to coverthis case by providing Lyapunov-based sufficient conditions thatensure input-to-state stability under small inputs, semigloballywith respect to initial conditions for discrete-time models thatarise from non-uniform sampling.