Reduced-order robust adaptive control design of uncertain SISO linear systems

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 orderreduction scheme is also applied to a class of single-input single-output linear systems with partly measured disturbances. Two examples are presented to illustrate the performance of the reduced-order controller in this paper. Copyright q 2007 John Wiley & Sons, Ltd.