Robust adaptive pole placement of first-order potentially inversely unstable continuous-time systems

This paper presents an indirect adaptive control scheme for nominally controllable unnecessarily inversely stable first-order continuous-time systems with unmodelled dynamics. The control objective is to achieve a bounded tracking-error between the system output and a reference signal. A recursive least squares algorithm with a suitable modification of the parameter estimates is used to obtain a controllable estimated model of the plant. The modification includes an hysteresis switching function to ensure the convergence of the modified parameters. Also, a relative dead-zone is used in the estimation algorithm for adaptation purposes.