Remarks on the stability of linear infinite-dimensional discrete-time systems

AbstractVarious results are presented which complement the existing theory of stability for linear (time-varying) infinite-dimensional discrete-time systems. The concept of generalized spectral radius of a (uniformly bounded) sequence of elements of a normed algebra is studied in detail, and several new formulas for computing this quantity are offered. Next, the problem of stability of perturbed systems is considered. Finally, a quantitative analysis of the so-called Perron condition is given