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A linear matrix inequality approach to H ∞ control
Author(s) -
Gahinet Pascal,
Apkarian Pierre
Publication year - 1994
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4590040403
Subject(s) - mathematics , linear matrix inequality , control theory (sociology) , parametrization (atmospheric modeling) , controller (irrigation) , convex optimization , lyapunov function , riccati equation , matrix (chemical analysis) , order (exchange) , regular polygon , mathematical optimization , control (management) , computer science , nonlinear system , mathematical analysis , partial differential equation , materials science , artificial intelligence , composite material , biology , geometry , quantum mechanics , agronomy , physics , radiative transfer , finance , economics
The continuous‐ and discrete‐time H ∞ 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 ∞ ‐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 ∞ 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 ∞ controllers opens new perspectives for the refinement of H ∞ design. Applications to cancellation‐free design and controller order reduction are discussed and illustrated by examples.