On stability of discrete-time systems under nonlinear time-varying perturbations

We give some explicit stability bounds for discrete-time systems subjected to time-varying and nonlinear perturbations. The obtained results are extensions of some well-known results in (Hinrichsen and Son in Int. J. Robust Nonlinear Control 8:1169-1188, 1998; Shafai et al. in IEEE Trans. Autom. Control 42:265-270, 1997) to nonlinear time-varying perturbations. Two examples are given to illustrate the obtained results. Finally, we present an Aizerman-type conjecture for discrete-time systems and show that this conjecture is valid for positive systems. MSC: 39A30, 93D09.