Numerical solution of the discrete-time, convergent, non-negative definite Lyapunov equation
Systems & Control Letters
The complex structured singular value
Automatica (Journal of IFAC) - Special issue on robust control
The projective method for solving linear matrix inequalities
Mathematical Programming: Series A and B
Computing a Hurwitz factorization of a polynomial
Journal of Computational and Applied Mathematics
Linear Prediction of Speech
Brief paper: Smooth trivial vector bundle structure of the space of Hurwitz polynomials
Automatica (Journal of IFAC)
Brief paper: A hierarchy of LMI inner approximations of the set of stable polynomials
Automatica (Journal of IFAC)
Determining the closest stable polynomial to an unstable one
IEEE Transactions on Signal Processing
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
| Hi-index | 22.14 |
Stability is a crucial property in the study of dynamical systems. We focus on the problem of enforcing the stability of a system a posteriori. The system can be a matrix or a polynomial either in continuous-time or in discrete-time. We present an algorithm that constructs a sequence of successive stable iterates that tend to a nearby stable approximation X of a given system A. The stable iterates are obtained by projecting A onto the convex approximations of the set of stable systems. Some possible applications for this method are correcting the error arising from some noise in system identification and a possible solver for bilinear matrix inequalities based on convex approximations. In the case of polynomials, a fair complexity is achieved by finding a closed form solution to first order optimality conditions.