ℒ1 adaptive control of system with unmatched disturbance by using eigenvalue assignment method

ℒ₁ adaptive architecture require the desired system dynamics to be minimum phase because the control law for these architectures performs explicit inversion of the desired dynamics. This paper presents a novel control law which relaxes this assumption and allows the desired system to be nonminimum-phase. This control law is inspired by the eigenvalue assignment method and does not require dynamic inversion of the desired system in the control law design. The disturbance will be compensated following a performance determined by the eigenvalues assigned to the controller. Choosing Appropriate eigenvalues will result in an reasonable fast response to cancel the disturbance.