Relaxations for Robust Linear Matrix Inequality Problems with Verifications for Exactness

Authors:
C. W. Scherer
Affiliations:
-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2005

Citing 0
Cited 14

Quadratic separation for feedback connection of an uncertain matrix and an implicit linear transformation

Automatica (Journal of IFAC)
Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem

Fuzzy Sets and Systems
A probabilistic analytic center cutting plane method for feasibility of uncertain LMIs

Automatica (Journal of IFAC)
Technical communique: On the degree of polynomial parameter-dependent Lyapunov functions for robust stability of single parameter-dependent LTI systems: A counter-example to Barmish's conjecture

Automatica (Journal of IFAC)
Parameter-dependent H2 and H∞ filter design for linear systems with arbitrarily time-varying parameters in polytopic domains

Signal Processing
Brief paper: An alternative Kalman-Yakubovich-Popov lemma and some extensions

Automatica (Journal of IFAC)
Convergent LMI relaxations for quadratic stabilizability and H∞ control of Takagi-Sugeno fuzzy systems

IEEE Transactions on Fuzzy Systems
Convex relaxations in circuits, systems, and control

IEEE Circuits and Systems Magazine
Exploiting sparsity in the sum-of-squares approximations to robust semidefinite programs

ACC'09 Proceedings of the 2009 conference on American Control Conference
Robust H2performance and design of discrete-time polytopic systems with LFT uncertainty

CCDC'09 Proceedings of the 21st annual international conference on Chinese control and decision conference
Brief paper: Stability and stabilization of aperiodic sampled-data control systems using robust linear matrix inequalities

Automatica (Journal of IFAC)
Homogeneous polynomially nonquadratic stabilization of discrete-time Takagi-Sugeno systems via nonparallel distributed compensation law

IEEE Transactions on Fuzzy Systems
Periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems

Automatica (Journal of IFAC)
Robust semidefinite programming problems with general nonlinear parameter dependence: Approaches using the DC-representations

Automatica (Journal of IFAC)

Quantified Score

Hi-index	0.02

Visualization

Abstract

Robust semidefinite programming problems with rational dependence on uncertainties are known to have a wide range of applications, in particular in robust control. It is well established how to systematically construct relaxations on the basis of the full block S-procedure. In general, such relaxations are expected to be conservative, but for concrete problem instances they are often observed to be tight. The main purpose of this paper is to suggest novel computationally verifiable conditions for when general classes of linear matrix inequality relaxations do not involve any conservatism. If the convex set of uncertainties is finitely generated, we suggest a novel sequence of relaxations which can be proved to be asymptotically exact. Finally, our results are applied to the particularly relevant robustness analysis problem for linear time-invariant dynamical systems affected by uncertainties that are full ellipsoidal or repeated and contained in intersections of disks or circles. This leads to extensions of known results on relaxation exactness for small block structures, including an elementary proof for tightness of standard structured singular value computations for three full complex uncertainty blocks.