Gain adjustment in a class of linear time-varying systems

Adjusting a vector gain using available signals in a system so that an error signal remains bounded in some sense is a fundamental problem in adaptive systems. Earlier literature has mostly dealt with specific configurations and time-invariant plants. An approach indicated in [3] introduced a general method of handling arbitrary location of adjustable gains in otherwise linear time-invariant systems. The present paper tackles arbitrary locations as well as time-varying linear systems where the time-variations are of the (constant +L2) type. It is shown that under relatively simple conditions involving strict passivity, the error is L2 bounded and other signals in the system are L?? bounded.