A linear matrix inequality approach toH∞control

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Abstract
The continuous‐ and discrete‐timeH∞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 allH∞‐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 ofH∞controllers and bear important connections with the controller order and the closed‐loop Lyapunov functions.Thanks to such connections, the LMI‐based characterization ofH∞controllers opens new perspectives for the refinement ofH∞design. Applications to cancellation‐free design and controller order reduction are discussed and illustrated by examples.