Yousong Luo

Companion matrices and their relations to Toeplitz and Hankel matrices

Abstract In this paper we describe some properties of companion matrices and demonstrate some special patterns that arisewhen a Toeplitz or a Hankel matrix is multiplied by a related companion matrix.We present a necessary and sufficient condition, generalizing known results, for a matrix to be the transforming matrix for a similarity between a pair of companion matrices. A special case of our main result shows that a Toeplitz or a Hankel matrix can be extended using associated companion matrices, preserving the Toeplitz or Hankel structure respectively.

Exact solutions to a two-block l1 optimal control problem

Abstract In this paper we illustrate some new ideas in the theory of l 1 –norm minimisation. A simple looking mathematical programming problem, namely the minimisation of the sum of the one norms of two signals connected by convolution constraints, is investigated. This describes an l 1 model matching problem for which there are no zero interpolation conditions, and just one rank interpolation condition. Despite its apparent simplicity, finding exact solutions for this problem is a challenging task. We extend the class of problems for which exact optimal solutions can be found by combining a primal/dual formulation with dynamic programming ideas. These solutions have the desirable feature of yielding a control law in feedback form.

On the uniqueness of solutions of spectral equations

We prove uniqueness of the viscosity solutions of the Dirichlet problem of the spectral equation

An application of C1,1 approximation to comparison principles for viscosity solutions of curvature equations☆

F(u)=f(\lambda[u])=\psi

Exact recursive estimation of linear systems subject to bounded disturbances

where

Exact recursive updating of uncertainty sets for discrete-time plants with a lag

\lambda[u]