Stability Margins of Adaptive Control Architecture

This technical note presents the ${cal L}_{1}$ adaptive control architecture for systems in the presence of unknown high-frequency gain with known sign, time-varying unknown parameters and disturbances. The ${cal L}_{1}$ adaptive controller leads to uniform performance bounds for the system's input and output signals, which can be systematically improved by increasing the adaptation rate. For constant unknown parameters, this result leads to analytically computable time-delay margin of a semiglobal nature.