Linear matrix inequality representation of sets

2 Linear Matrix Inequality Representation of Sets

This article concerns the question: which subsets of R can be represented with Linear Matrix Inequalities, LMIs? This gives some perspective on the scope and limitations of one of the most powerful techniques commonly used in control theory. Also before having much hope of representing engineering problems as LMIs by automatic methods one needs a good idea of which problems can and cannot be re...

2 Linear Matrix Inequality Representation of Sets

A Linear Matrix Inequality Approach

This paper addresses the problem of designing stabilizing controllers that minimize the 7 l ~ norm of a certain closed-loop transfer function while maintaining the C1 norm of a different transfer function below a prespecified level. This problem arises in the context of rejecting both stochastic as well as bounded persistent disturbances. Alternatively, in a robust control framework it can be t...

Polynomial Matrix Inequality and Semidefinite Representation

Consider a convex set S = {x ∈ D : G(x) o 0} where G(x) is a symmetric matrix whose every entry is a polynomial or rational function, D ⊆ R is a domain on which G(x) is defined, and G(x) o 0 means G(x) is positive semidefinite. The set S is called semidefinite representable if it equals the projection of a higher dimensional set which is defined by a linear matrix inequality (LMI). This paper s...

A Linear Matrix Inequality Approach toH 1

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 controllers. The solvability conditions invol...