Asymptotic characterizations of input–output-to-state stability for discrete-time systems

We establish the equivalence between global detectability and output-to-state stability for difference inclusions with outputs, and we present equivalent asymptotic characterizations of input–output-to-state stability for discrete-time nonlinear systems. These new stability characterizations for discrete-time systems parallel what have been developed for continuous-time systems in Angeli et al. [Uniform global asymptotic stability of differential inclusions, J. Dynamical Control Systems 10 (2004) 391–412] and Angeli et al. [Seperation principles for input–output and integral-input-to-state stability, SIAM J. Control Optim. 43 (2004) 256–276].