ON TWO THEOREMS REGARDING EXPONENTIAL STABILITY

There are two remarkable results in the theory of stability of dynamical systems which were obtained by E. A. Barbashin in 1967 and R. Datko in 1970. After the seminal researches of Datko and Barbashin, there has been a great number of works devoted to this results. For the case of discrete-time systems analogous results have been obtained. This paper will give the new versions which unify the discrete-time versions of Barbashin’s theorem and Datko’s theorem.