Observer-Based Quadratic Guaranteed Cost Control for Linear Uncertain Systems with Control Gain Variation

This study proposes a method for designing observer-based quadratic guaranteed cost controllers for linear uncertain systems with control gain variations. In the proposed approach, an observer is designed, and then a feedback controller that ensures the upper bound on the given quadratic cost function is derived. This study shows that sufficient conditions for the existence of the observer-based quadratic guaranteed cost controller are given in terms of linear matrix inequalities. A sub-optimal quadratic guaranteed cost control strategy is also discussed. Finally, the effectiveness of the proposed controller is illustrated by a numerical example. The result shows that the proposed controller is more effective than conventional methods even if system uncertainties and control gain variations exist.