Nonuniform in Time Input-to-State Stability and the Small-Gain Theorem

For time-varying control systems various equivalent characterizations of the nonuniform in time input-to-state stability (ISS) property are established. These characterizations enable us to derive sufficient conditions for nonuniform in time ISS concerning composite time-varying systems. Our main result generalizes the well-known small-gain theorem due to Jiang-Teel-Praly for autonomous systems under the presence of uniform in time ISS.