INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING Int. J. Adapt. Control Signal Process. 2004; 00:1–46 Prepared using acsauth.cls [Version: 2002/11/11 v1.00] Reduced-order robust adaptive control design of uncertain SISO linear systems Qingrong Zhao, Zigang Pan ∗ , Emmanuel Fernandez ∗∗ Department of Electrical and Computer Engineering and Computer Science, University of Cincinnati, Cincinnati, OH 45221-0030. SUMMARY In this paper, a stability and robustness preserving adaptive controller order reduction method is developed for a class of uncertain linear systems affected by system and measurement noises. In this method, we immediately start the integrator backstepping procedure of the controller design without first stabilizing a filtered dynamics of the output. This relieves us from generating the reference trajectory for the filtered dynamics of the output and thus reducing the controller order by n, n being the dimension of the system state. The stability of the filtered dynamics is indirectly proved via an existing state signal. The trade-off for this order reduction is that the worst-case estimate for the expanded state vector has to be chosen as a suboptimal choice, rather than the optimal choice. It is shown that the resulting reduced-order adaptive controller preserves the stability and robustness properties of the full-order adaptive controller in disturbance attenuation, boundedness of closed- loop signals, and output tracking. The proposed order-reduction scheme is also applied to a class of SISO linear systems with partly measured disturbances. Two examples are presented to illustrate the performance of the reduced-order controller in the paper. key words: adaptive control; nonlinear H ∞ control; cost-to-come function; integrator backstepping 1. INTRODUCTION Adaptive control has been an important research topic in control theory. Based on the approach adopted to address the problem, adaptive control design may be classified into three categories: certainty equivalence (CE) based design, nonlinear adaptive control design, and worst-case analysis (WCA) based design. Early development of adaptive control since 1970s has been dominated by CE principle [2, 3], which decouples the parameter estimation design from the control design, by making use of some standard parameter estimators and supplying the estimates to control law as if they * Formerly associated with the Department of Electrical and Computer Engineering and Computer Science at the University of Cincinnati, Cincinnati, OH. ** Corresponding author: Department of Electrical and Computer Engineering and Computer Science, 814 Rhodes Hall, Mail Loc. 0030, University of Cincinnati, Cincinnati, OH 45221-0030. Tel: 513-556-4785; Fax: 513-556-7326; Email: emmanuel@ececs.uc.edu. Copyright c  2004 John Wiley & Sons, Ltd.