Adaptive regulation of MIMO linear discrete-time systems without requiring a persistent excitation

An adaptive regulator which does not require a persistent excitation is developed for multiinput multioutput (MIMO) linear discrete-time systems. The assumptions on the plant are 1) an upper bound on the system dimension is known; 2) the unknown system parameters belong to known bounded intervals; 3) the plant is stabilizable for all possible values of the unknown system parameters. The stabilizability condition can be tested before the system is put into operation. A recursive parameter estimation scheme is given which forces the parameter estimates to converge to the known intervals. Using this estimator, an adaptive regulator is derived which results in a globally-stable closed-loop system.