New LMI conditions for static output feedback synthesis with multiple performance objectives

Abstract

The static output feedback synthesis problem is considered with ℋ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> and generalized ℋ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> performance objectives. New sufficient LMI conditions are derived for guaranteeing the required performance objectives. These conditions also depend on scalar parameters that need to be fixed beforehand. The output feedback gain matrix is computed from the involved matrix variables without the use of system matrices. Hence the conditions can directly be used to solve the multi-objective synthesis problem also for parameter-dependent systems with constant or parameter-dependent gain matrices. The method is illustrated in the adaptive cruise control problem.