LMI Methods in Design

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Author Index
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Control Synthesis with Dynamic Integral Quadratic Constraints - LMI Approach

Authors:

Chung-Yao Kao, Muralidhar Ravuri, Alexander Megretski,

Volume: 1, Page 1477 Paper number 1981

Abstract:

In this paper, we consider the control synthesis problem when the disturbance input w is within a set defined by several dynamic Integral Quadratic Constraints (IQCs). We show that the condition on the existence of a stabilizing controller can be expressed as a set of Linear Matrix Inequalities (LMIs). We also show that the stabilizing controllers, if exist, have the dimension no larger than the sum of the dimension of the open-loop system and the multipliers in IQCs.

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Rank-One LMIs and Lyapunov's Inequality

Authors:

Didier Henrion, Gjerrit Meinsma,

Volume: 1, Page 1483 Paper number 1633

Abstract:

We describe a new proof of the well-known Lyapunov's matrix inequality about the location of the eigenvalues of a matrix in some region of the complex plane. The proof makes use of standard facts from quadratic and semi-definite programming. Links are established between the Lyapunov matrix, rank-one LMIs and the Lagrange multiplier arising in duality theory.

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Analysis, Eigenstructure Assignment and H_2 Multi-Channel Synthesis with Enhanced LMI Characterizations

Authors:

Pierre Apkarian, Hoang Duong Tuan, Jacques Bernussou,

Volume: 1, Page 1489 Paper number 1846

Abstract:

The paper 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 addition to the classical linearizing transformations on the controller data. For a wide range of problems including robust analysis and synthesis, multi-chanel H2 state and output-feedback syntheses, the approach leads to potentially less conservative LMI characterizations. This comes from the fact that the technical restriction of using a single Lyapunov function is to some extent ruled out in this new approach. Moreover, the approach offers new potentials for problems that cannot be handled using earlier techniques. As an instance, the eigenstructure assignment problem blended with Lyapunov-type constraints is given a simple and tractable formulation.

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A LMI Approach To Robust Observer Design For Linear Time-Delay Systems

Authors:

Anas Fattouh, Olivier Sename, Jean-Michel Dion,

Volume: 1, Page 1495 Paper number 1481

Abstract:

This paper is concerned with a robust observer design for linear time-delay systems via linear matrix inequality approach. The proposed method not only guarantees the stability of the proposed observer, but also reduces the effects of different unstructured uncertainties (like the additive uncertainty, the input multiplicative uncertainty,...) on the estimated error.

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An LMI-Based Approach For Characterizing The Solution Set Of Polynomial Systems

Authors:

Graziano Chesi, Andrea Garulli, Alberto Tesi, Antonio Vicino,

Volume: 1, Page 1501 Paper number 1868

Abstract:

This paper considers the problem of solving certain classes of polynomial systems. This is a well known problem in control system analysis and design. A novel approach is developed as a possible alternative to the commonly employed algebraic geometry and homotopy methods. The first result of the paper shows that the solution set of the polynomial system belongs to the kernel of a symmetric matrix. Such a matrix is obtained via the solution of a suitable Linear Matrix Inequality (LMI) involving the maximization of the minimum eigenvalue of an affine family of symmetric matrices. The second result concerns the computation of the solutions from the kernel of the obtained matrix. In particular, it is shown that the solutions can be recovered quite easily if the dimension of the kernel is smaller than the degree of the polynomial system. Finally, some application examples are illustrated to show the features of the approach and to make a brief comparison with the algebraic geometry techniques.

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An LMI Approach For Robust Stability Of Linear Uncertain Systems With Time-Varying Multiple State Delays

Authors:

Te-Jen Su, Chien-Yu Lu, Gw-Jia Jong,

Volume: 1, Page 1507 Paper number 8003

Abstract:

This paper provides new stability criteria for a class of uncertain linear time-delay systems with time-varying delays. Based on Lyapunov-Krasovskii functionals combining with LMI techniques, improved delay-dependent robust stability criteria, which are given in terms of quadratic forms of state and LMI, are derived. Our results shown by an example are less conservative than the existing stability criteria.

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