E. Feron

Control System Analysis and Synthesis via Linear Matrix Inequalities

A wide variety of problems in systems and control theory can be cast or recast as convex problems that involve linear matrix inequalities (LMIs). For a few very special cases there are analytical solutions to these problems, but in general they can be solved numerically very efficiently. In many cases the inequalities have the form of simultaneous Lyapunov or algebraic Riccati inequalities; such problems can be solved in a time that is comparable to the time required to solve the same number of Lyapunov or Algebraic Riccati equations. Therefore the computational cost of extending current control theory that is based on the solution of algebraic Riccati equations to a theory based on the solution of (multiple, simultaneous) Lyapunov or Riccati inequalities is modest. Examples include: multicriterion LQG, synthesis of linear state feedback for multiple or nonlinear plants (multi-model control), optimal transfer matrix realization, norm scaling, synthesis of multipliers for Popov-like analysis of systems with unknown gains, and many others. Full details can be found in the references cited.

On Maximizing a Robustness Measure for Structured Nonlinear Perturbations

In this paper, we propose a robustness measure for LTI systems with causal, nonlinear diagonal perturbations with finite L2-gain. We propose an algorithm to reliably compute this quantity. We show how to find a state-feedback controller that achieves the global maximum of the robustness measure.

History of linear matrix inequalities in control theory

The purpose of this paper is to give a historical view of linear matrix inequalities in control and system theory. Not surprisingly, it appears that LMIs have been,involved in some of the major events of control theory. With the advent of powerful convex optimization techniques, LMIs are now about to become an important practical tool for future control applications.

Design of stabilizing state feedback for delay systems via convex optimization

For linear systems with delays, the authors define a new class of Lyapunov-like functionals that can be used to prove stability. They also show how one can design a stabilizing (delayed) state feedback for delay systems using these functionals and convex optimization techniques. It is shown how the problem of the design of a stabilizing (delayed) state-feedback can be posed as a convex feasibility problem.<<ETX>>

Computing Bounds for the Structured Singular Value via an Interior Point Algorithm

We describe an interior point algorithm for computing the upper bound for the structured singular value described in [1]. We demonstrate the performance of the algorithm on a simple example.