Adaptive unit-vector law with time-varying gain for finite-time parameter estimation in LTI systems

A continuation of previous authors' work on adaptive parameter estimation for linear dynamical systems having irrational transfer function is presented in this work. An original modification of the gradient algorithm, inspired by the variable structure control techniques and additionally featuring a time-varying adaptation gain, is presented and analyzed using Lyapunov techniques. The exposition is illustrated by several numerical examples which illustrate the effectiveness of the proposed algorithm.