Summation-type conditions for uniform asymptotic convergence in discrete-time systems: applications in identification

We establish summation-type conditions to ensure the uniform convergence of discrete-time systems, parameterized in the sampling time. The main results are analogous to previous results obtained in the domain of continuous-time systems and that we have referred to as "integral conditions". The sufficient conditions that we present here can also be interpreted as conditions for convergence of series. Our main results are also useful for design of sampled-data controllers via approximate models; for illustration, we present two results on control design reminiscent of common problems arising in identification and adaptive control.