A Linear Matrix Inequality Approach to H 1 Control

The continuous-and discrete-time H 1 control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems , and an LMI-based parametrization of all H 1-suboptimal controllers, including reduced-order controllers. The solvability conditions involve Riccati inequalities rather than the usual indee-nite Riccati equations. Alternatively, these conditions can be expressed as a system of three LMI's. EEcient convex optimization techniques are available to solve this system. Moreover, its solutions parametrize the set of H 1 controllers and bear important connections with the controller order and the closed-loop Lyapunov functions. Thanks to such connections, the LMI-based characterization of H 1 controllers opens new perspectives for the reenement of H 1 design. Applications to cancellation-free design and controller order reduction are discussed and illustrated by examples.