2.3. H∞ Performance 3. Controller Design Using Linear Matrix Inequalities 3.1. Linearizing Change of Variables – State Feedback 3.2. Linearizing Change of Variables Output Feedback 3.3. LMI Approach to Multiobjective Design 3.4. Existence of Solutions and Conservatism of Design 4. Illustrative Design Example: Robust Control of a Power System Stabilizer 4.1. Problem Description 4.2. Design Speci...

We present an application of a new controller order reduction technique with stability and performance preservation based on linear matrix inequality optimization to an active suspension system. In this technique, the rank of the residue matrix of a proper rational approximation of a high-order Hoo controller subject to the H,,norm of a frequency-weighted error between the approximated controll...

Let A(x) = A0 + x1A1 + · · · + xnAn be a linear matrix, or pencil, generated by given symmetric matrices A0, A1, . . . , An of size m with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a convex semialgebraic set called spectrahedron, described by a linear matrix inequality (LMI). We design an exact algorithm that, up to genericity assumptions on th...

For iterative sequences that converge to the solution set of a linear matrix inequality, we show that the distance of the iterates to the solution set is at most O(2 ?d). The nonnegative integer d is the so{called degree of singularity of the linear matrix inequality, and denotes the amount of constraint violation in the iterate. For infeasible linear matrix inequalities, we show that the minim...

Let A be a Hermitian matrix, let be a normalized positive linear map and let f be a continuous real valued function. Real constants and such that (f(A)) f(((A)) (f(A)) are determined. If f is matrix convex then can be taken to be 1. A uniied approach is proposed so that the problem of determining and is reduced to solving a single variable convex minimization problem. As an illustration, the re...

A necessary and suucient condition is proposed for the existence of a xed polynomial p(s) such that the rational function p(s)=q(s) is robustly strictly positive real when q(s) is a given Hurwitz polynomial with polytopic uncertainty. It turns out that the whole set of candidates p(s) is a convex subset of the cone of positive semideenite matrices, resulting in a straightforward strictly positi...