A LINEAR MATRIX INEQUALITY APPROACH TO H-INFINITY CONTROL

The continuous- and discrete-time H(infinity) 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(infinity)-suboptimal controllers, including reduced-order controllers. The solvability conditions involve Riccati inequalities rather than the usual indefinite Riccati equations. Alternatively, these conditions can be expressed as a system of three LMIs. Efficient convex optimization techniques are available to solve this system. Moreover, its solutions parametrize the set of H(infinity) 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(infinity) controllers opens new perspectives for the refinement of H(infinity) design. Applications to cancellation-free design and controller order reduction are discussed and illustrated by examples.