The Non-uniform in Time Small-Gain Theorem for a Wide Class of Control Systems with Outputs

Small-gain statements play a key role in system analysis. These results state that the interconnection of two stable systems is stable provided that the closed loop gain is less than unity. This intuitively satisfying statement can be made rigorous in a number of ways depending on the notion of stability and the family of systems under consideration. Such results were originally given in the 1960’s by Zames [6, 7], Sandberg [4] and others who addressed stability of input-output systems by the use of linear gains.