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Branch-and-bound algorithm for computing the minimum stability degree of parameter-dependent linear systems
Branch and bound algorithm linear systems a robust nonlinear and linear system stability the parameters of linear system
2015/8/12
We consider linear systems with unspecified parameters that lie between given upper and lower bounds. Except for a few special cases, the computation of many quantities of interest for such systems ca...
On computing the worst-case peak gain of linear systems
SISO discrete-time LTI systems computation of `1-gain discrete-time systems with diagonal perturbations worst-case `1-gain.
2015/8/12
Based on the bounds in the paper by Boyd and Doyle (Comparison of peak and RMS gains for discrete-time systems, Systems and Control Letters, 9:1-6), we present simple upper and lower bounds for the el...
Linear matrix inequalities in system and control theory
Linear matrix inequality system the control theory and linear matrix inequality affine combination symmetric positive semidefinite matrix
2015/8/12
A wide variety of problems in system and control theory can be formulated (or reformulated) as convex optimization problems involving linear matrix inequalities, that is, constraints requiring an affi...
Control systems analysis and synthesis via linear matrix inequalities
Control theory and linear matrix inequality the numerical algebraic riccati inequality lyapunov
2015/8/12
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 sol...
Method of centers for minimizing generalized eigenvalues
quasiconvex nondifferentiable optimization generalized eigenvalue linear fractional programming analytic center method of centers interior point method logarithmic barrier Newton algorithm path-following method ellipsoidal approximations
2015/8/12
We consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices, each of which depends affinely on the decision variables. Although this problem may appear spe...
History of linear matrix inequalities in control theory
Linear matrix inequality control control theory tool control applications
2015/8/12
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...
Optimal linear static control with moment and yield objectives
Linear static control gaussian distribution convex optimization
2015/8/11
This report describes how to optimize linear static control problems involving first and second moments and yield objectives for Gaussian distributions. These problems can be cast as second-order cone...
Robust solutions to l1, l2, and l_infinity uncertain linear approximation problems using convex optimization
Linear random and uncertain data convex optimization
2015/8/11
We present minimax and stochastic formulations of some linear approximation problems with uncertain data in R^n equipped with the Euclidean (l2), Absolute-sum (l1) or Chebyshev (l-infinity) norms. We ...
Multiobjective H_2/H_infinity-optimal control via finite dimensional Q-parametrization and linear matrix inequalities
Controller design convex semidefinite programming impulse response
2015/8/11
The problem of multi-objective H2/H-infinity optimal controller design is reviewed. There is as yet no exact solution to this problem. We present a method based on that proposed by Scherer. The proble...
Control-relevant experiment design: a plant-friendly, LMI-based approach
Semidefinite programming linear matrix inequality
2015/8/11
The non-convex control-relevant experiment design developed in earlier works is transformed to a semidefinite program with linear matrix inequality constraint. As a result, the computational burden is...
Determinant maximization with linear matrix inequality constraints
Matrix linear matrix inequality (lmi) computational geometry statistics system identification communication theory
2015/8/11
The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment desig...
Least-squares covariance matrix adjustment
Symmetric matrices linear equations inequalities the original matrix
2015/8/10
We consider the problem of finding the smallest adjustment to a given symmetric n by n matrix, as measured by the Euclidean or Frobenius norm, so that it satisfies some given linear equalities and ine...
Pareto optimal linear classification
Linear classifier probability weigh gaussian distribution
2015/8/10
We consider the problem of choosing a linear classifier that minimizes misclassification probabilities in two-class classification, which is a bi-criterion problem, involving a trade-off between two o...
Enhancing sparsity by reweighted l1 minimization
1-Minimization ·Iterative reweighting Underdetermined systems of linear equations·Compressive sensing Dantzig selector· Sparsity FOCUSS
2015/8/10
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constraine...
Performance bounds for linear stochastic control
Stochastic control Model predictive control Linear matrix inequality Convex optimization
2015/8/10
We develop computational bounds on performance for causal state feedback stochastic control with linear dynamics, arbitrary noise distribution, and arbitrary input constraint set. This can be very use...