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- Pierre Apkarian
- 1994

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)

An important class of linear time-varying systems consists of plants where the state-space matrices are xed functions of some time-varying physical parameters. Small Gain techniques can be applied to such systems to derive robust time-invariant controllers. Yet, this approach is often overly conservative when the parameters undergo large variations during… (More)

- Pierre Apkarian, Pascal Gahinet, Greg Becker
- Automatica
- 1995

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)

- Pierre Apkarian, Richard J. Adams
- IEEE Trans. Contr. Sys. Techn.
- 1998

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)

- Hoang Duong Tuan, Pierre Apkarian, Tatsuo Narikiyo, Yasuhiro Yamamoto
- IEEE Trans. Fuzzy Systems
- 2001

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)

- Mahmoud Chilali, Pascal Gahinet, Pierre Apkarian
- IEEE Trans. Automat. Contr.
- 1999

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)

- Pierre Apkarian, Dominikus Noll
- IEEE Trans. Automat. Contr.
- 2006

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)

- Pierre Apkarian, Hoang Duong Tuan, Jacques Bernussou
- IEEE Trans. Automat. Contr.
- 2001

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)

- Hoang Duong Tuan, Pierre Apkarian, Truong Q. Nguyen
- IEEE Trans. Signal Processing
- 2001

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)

- Pierre Apkarian, Hoang Duong Tuan
- SIAM J. Control and Optimization
- 2000

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)