Further subadditive matrix inequalities

Further Results on “Robust MPC Using Linear Matrix Inequalities”

This paper presents a novel method for designing the terminal cost and the auxiliary control law (ACL) for robust MPC of uncertain linear systems, such that ISS is a priori guaranteed for the closed-loop system. The method is based on the solution of a set of LMIs. An explicit relation is established between the proposed method and H∞ control design. This relation shows that the LMI-based optim...

From Subadditive Inequalities of Singular Values to Triangle Inequalities of Canonical Angles

Kingman's Subadditive Ergodic Theorem Kingman's Subadditive Ergodic Theorem

A simple proof of Kingman’s subadditive ergodic theorem is developed from a point of view which is conceptually algorithmic and which does not rely on either a maximal inequality or a combinatorial Riesz lemma.

Solubility of Matrix Inequalities

An important part is played in the theory of control by special matrix equations [i], and also by the matrix inequalities associated with them. The solutions of these equations or inequalities allow us to construct Lyapunov functions for nonlinear systems of automatic regulation, and to solve problems of the synthesis of optimal control with quadratic quality criterion. Convenient and effective...

On some matrix inequalities

The arithmetic-geometric mean inequality for singular values due to Bhatia and Kittaneh says that 2sj(AB ∗) ≤ sj(A∗A + B∗B), j = 1, 2, . . . for any matrices A,B. We first give new proofs of this inequality and its equivalent form. Then we use it to prove the following trace inequality: Let A0 be a positive definite matrix and A1, . . . , Ak be positive semidefinite matrices. Then tr k ∑