Warrington, PhD, P.E., University of Tennessee at Chattanooga Introduction Glover, Robust and Optimal Control, Prentice-Hall, Englewood Cliffs, NJ, 1996.By Don C. Vandewalle, A nonsmooth optimisation approach for the stabilisation of time-delay systems, ESAIM Control Optim. Embree, Spectra and Pseudospectra – The Behavior of Nonnormal Matrices, Princeton University Press, Princeton, NJ, 2005. OMSOE2 1055-6788 Crossref ISI Google Scholar Sturm, Using SeDuMi $1.02$, a matlab toolbox for optimization over symmetric cones, Optim. Apkarian, Spectral bundle methods for nonconvex maximum eigenvalue functions. IJCOAZ 0020-7179 Crossref ISI Google Scholar Roose, An eigenvalue based approach for the robust stabilization of linear time-delay systems, Internat. Orsi, H-infinity synthesis via a nonsmooth, nonconvex optimization approach, Pac. Löfberg, YALMIP: A toolbox for modeling and optimization in matlab, in Proceedings of the CACSD Conference, Taipei, Taiwan, 2004. Loan, The sensitivity of the matrix exponential, SIAM J. JCAMDI 0377-0427 Crossref ISI Google Scholar Loan, The ubiquitous Kronecker product, J. Leibfritz, COMPl$_e$ib: COnstraint Matrix-optimization Problem Library – A Collection of Test Examples for Nonlinear Semidefinite Programs, Control System Design and Related Problems, Technical report, Universität Trier, Trier, Germany, 2004. Lancaster, Explicit solutions of linear matrix equations, SIAM Rev., 12 ( 1970), pp. Graham, Kronecker Products and Matrix Calculus With Applications, Halsted Press, John Wiley and Sons, New York, 1981. 169, American Mathematical Society, Providence, RI, 1997. Godunov, Ordinary Differential Equations with Constant Coefficient, Trans. Noll, Stability Optimization of Hybrid Periodic Systems via a Smooth Criterion, Technical report 07-97, ESAT-SISTA, K.U.Leuven, Belgium, 2007. MHPGA4 0025-5610 Crossref ISI Google Scholar Overton, Variational analysis of non-Lipschitz spectral functions, Math. Overton, Differential properties of the spectral abscissa and the spectral radius for analytic matrix-valued mappings, Nonlinear Anal., 23 ( 1994), pp. Overton, A robust gradient sampling algorithm for nonsmooth, nonconvex optimization, SIAM J. IJNADH 0272-4979 Crossref ISI Google Scholar Overton, Robust stability and a criss-cross algorithm for pseudospectra, IMA J. Overton, Optimization and pseudospectra, with applications to robust stability, SIAM J. Overton, A nonsmooth, nonconvex optimization approach to robust stabilization by static output feedback and low-order controllers, in Proceedings of 4th IFAC Symposium on Robust Control Design, Milan, Italy, 2003, pp. LAAPAW 0024-3795 Crossref ISI Google Scholar Overton, Two numerical methods for optimizing matrix stability, Linear Algebra Appl., 351 ( 2002), pp. Overton, HIFOO-A matlab package for fixed-order controller design and H-infinity optimization, in Proceedings of the 5th IFAC Symposium on Robust Control Design, Toulouse, France, 2006. Brent, Algorithms for Minimization without Derivatives, Prentice-Hall, Englewood Cliffs, NJ, 1973. NUMMA7 0029-599X Crossref ISI Google Scholar Xu, A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils, Numer. CACMA2 0001-0782 Crossref ISI Google Scholar Stewart, Solution of the matrix equation $AX + XB = C$, Comm. IETAA9 0018-9286 Crossref ISI Google Scholar Vandenberghe, Semidefinite programming duality and linear time-invariant systems, IEEE Trans. EJCOFU 0947-3580 Crossref ISI Google Scholar Noll, Nonsmooth optimization for multidisk H-infinity synthesis, Eur. Noll, Nonsmooth H-infinity synthesis, IEEE Trans. In both cases, additional equality and inequality constraints on the variables can be naturally taken into account in the optimization problem. The latter problem can be interpreted as an $H_2$-norm minimization problem, and its solution additionally implies an upper bound on the corresponding $H_\infty$-norm or a lower bound on the distance to instability. We therefore propose a new stability measure, namely, the smoothed spectral abscissa $\tilde\alpha_(A(x))\leq0$ is still satisfied. It is well known that the minimization of the spectral abscissa function $\alpha(A)$ gives rise to very difficult optimization problems, since $\alpha(A)$ is not everywhere differentiable and even not everywhere Lipschitz. This paper concerns the stability optimization of (parameterized) matrices $A(x)$, a problem typically arising in the design of fixed-order or fixed-structured feedback controllers.
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