Pierre Apkarian

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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(More)
This paper is concerned with the design of gain-scheduled controllers with guaranteed H1 performance for a class of Linear Parameter-Varying (LPV) plants. Here the plant state-space matrices are assumed to depend aanely on a vector of time-varying real parameters. Assuming real-time measurement of these parameters, they can be fed to the controller to(More)
This paper is concerned with the design of gain-scheduled controllers for Linear Parameter-Varying systems. Two alternative LMI characterizations are investigated. Both characterizations are amenable to a nite number of LMI conditions either via a gridding of the parameter range or via grid-free techniques which rely on multi-convexity concepts.(More)
This paper proposes different parameterized linear matrix inequality (PLMI) characterizations for fuzzy control systems. These PLMI characterizations are, in turn, relaxed into pure LMI programs, which provides tractable and effective techniques for the design of suboptimal fuzzy control systems. The advantages of the proposed methods over earlier ones are(More)
This paper discusses analysis and synthesis techniques for robust pole placement in LMI regions, a class of convex regions of the complex plane that embraces most practically useful stability regions. The focus is on linear systems with static uncertainty on the state matrix. For this class of uncertain systems, the notion of quadratic stability and the(More)
We develop nonsmooth optimization techniques to solve H∞ synthesis problems under additional structural constraints on the controller. Our approach avoids the use of Lyapunov variables and therefore leads to moderate size optimization programs even for very large systems. The proposed framework is very versatile and can accommodate a number of challenging(More)
This note describes a new framework for the analysis and synthesis of control systems, which constitutes a genuine continuous-time extension of results that are only available in discrete time. In contrast to earlier results the proposed methods involve a specific transformation on the Lyapunov variables and a reciprocal variant of the Projection Lemma, in(More)
Several challenging problems of robust filtering are addressed in this paper. First of all, we exploit a new LMI (Linear Matrix Inequality) characterization of minimum variance or of H2 performance, and demonstrate that it allows the use of parameterdependent Lyapunov functions while preserving tractability of the problem. The resulting conditions are less(More)
A wide variety of problems in control system theory fall within the class of parameterized Linear Matrix Inequalities (LMIs), that is, LMIs whose coeecients are functions of a parameter connned to a compact set. Such problems, though convex, involve an innnite set of LMI constraints, hence are inherently diicult to solve numerically. This paper investigates(More)