LINEAR-QUADRATIC SUBOPTIMAL CONTROL WITH STATIC OUTPUT-FEEDBACK

This paper considers the design of a stabilizing static output feedbac k gain which keeps the linear quadratic (LQ) performance index less th an a specified number (we call this an 'LQ suboptimal controller'). Ex istence of such a controller is shown to be equivalent to the existenc e of a positive-definite matrix P such that P satisfies two linear mat rix inequalities (LMIs) while P-1 satisfies another LMI. All LQ subopt imal controllers are explicitly parameterized by the freedom in the ch oice of the positive-definite matrix P satisfying the LMIs, and an arb itrary positive scalar and an arbitrary matrix of fixed dimension with a norm bound. A modified version of the min/max algorithm is given to find a positive-definite solution P to the LMIs.