A robust adaptive pole-placement controller without strictly positive real condition

This paper considers the adaptive pole-placement control problem for system (1) with unmodelled dynamics eta(n) dominated by a small constant epsilon multiplied by a quantity independent of epsilon but tending to infinity as the past input, output, and noise grow. Using bounded external excitation and randomly varying truncation techniques, we give a design method of adaptive pole-placement controller. It is shown that the closed-loop system is globally stable, the estimation error for the parameter contained in the modelled part is of order epsilon, and the closed-loop system under the adaptive pole-placement control law is suboptimal in the sense of lim sup(n-->infinity) 1/n Sigma(i=0)(n) (A*(z)y(n) - L(z)C(z)w(n) - B(z)R(z)y(n)*)(2) less than or equal to O(epsilon(2)) + y(2) Sigma(j=1)(q) b(j)(2) while the SPR condition used usually in other papers is replaced by a stability condition. Copyright (C) 2001 John Wiley Sons, Ltd.