Adaptive stabilization of discrete-time systems using linear periodically time varying controllers

A direct adaptive scheme based on the use of linear time-varying periodic controllers is proposed which estimates online the periodic coefficients of the controller. It is shown that adaptive stabilization is attained for all possibly nonstably invertible plants of known order but unknown delay. Although no appeal is made to persistency of excitation arguments, a provision is needed to avoid the singularity of an estimated matrix, this property being required only for the analysis and not the control calculations.