Author
Jacques Bernussou
Bio: Jacques Bernussou is an academic researcher from Hoffmann-La Roche. The author has contributed to research in topics: Linear system & Robust control. The author has an hindex of 17, co-authored 55 publications receiving 4149 citations.
Papers published on a yearly basis
Papers
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TL;DR: In this paper, a new robust stability condition for uncertain discrete-time systems with convex polytopic uncertainty is given, which enables to check stability using parameter-dependent Lyapunov functions which are derived from LMI conditions.
1,456 citations
TL;DR: In this article, a new LMI-based sufficient condition for the existence of parameter-dependent Lyapunov functions is proposed, which generalises previously published conditions and appears to be promising for robust multi-objective performance analysis and control synthesis purposes.
711 citations
TL;DR: It is shown that extending the new discrete time stability condition proposed by de Oliveira et al. to the case of time varying uncertainty leads to a necessary and sufficient condition for the computation of such a Lyapunov function.
657 citations
TL;DR: In this paper, the authors present a new procedure for continuous and discrete-time linear control systems design, which consists of the definition of a convex programming problem in the parameter space that, when solved, provides the feedback gain.
Abstract: This paper presents a new procedure for continuous and discrete-time linear control systems design. It consists of the definition of a convex programming problem in the parameter space that, when solved, provides the feedback gain. One of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation, yielding solutions to problems that have raised a great deal of interest within the last few years. This is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices. In this last case, necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and, to the authors’ knowledge, this is one of the first numerical procedures able to handle and solve this interesting design problem for high-order, continuous-time or discrete-time linear models. The theory is illustrated by examples.
348 citations
TL;DR: It is shown how to use a new parameter dependent Lyapunov matrix procedure to determine high performance H2 robust filters by solving a linear problem constrained by linear matrix inequalities (LMIs).
Abstract: Robust filtering of linear time-invariant discrete-time uncertain systems is investigated through a new parameter dependent Lyapunov matrix procedure. Its main interest relies on the fact that the Lyapunov matrix used in stability checking does not appear in any multiplicative term with the uncertain matrices of the dynamic model. We show how to use such an approach to determine high performance H2 robust filters by solving a linear problem constrained by linear matrix inequalities (LMIs). The results encompass the previous works in the quadratic Lyapunov setting. Numerical examples illustrate the theoretical results.
214 citations
Cited by
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Book•
01 Jan 1994
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
Abstract: Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.
11,085 citations
TL;DR: This paper presents a new approach for robust MPC synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation, and shows that the feasible receding horizon state-feedback control design robustly stabilizes the set of uncertain plants.
2,329 citations
TL;DR: An overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems is provided.
2,186 citations
2,140 citations
TL;DR: A survey on recent developments (or state of the art) of analysis and design of model based fuzzy control systems based on the so-called Takagi-Sugeno fuzzy models or fuzzy dynamic models.
Abstract: Fuzzy logic control was originally introduced and developed as a model free control design approach. However, it unfortunately suffers from criticism of lacking of systematic stability analysis and controller design though it has a great success in industry applications. In the past ten years or so, prevailing research efforts on fuzzy logic control have been devoted to model-based fuzzy control systems that guarantee not only stability but also performance of closed-loop fuzzy control systems. This paper presents a survey on recent developments (or state of the art) of analysis and design of model based fuzzy control systems. Attention will be focused on stability analysis and controller design based on the so-called Takagi-Sugeno fuzzy models or fuzzy dynamic models. Perspectives of model based fuzzy control in future are also discussed
1,575 citations