An algorithm for nonconservative stability bounds computation for systems with nonlinearly correlated parametric uncertainties

The problem of robust stability analysis of linear dynamic systems with uncertain physical parameters entering polynomially in the state equation matrices is considered. A method is proposed for solving both the problems of checking stability of a family of matrices generated by a box in parameter space and that of computing maximal box domains of given shape in parameter space generating only stable matrices. A globally convergent optimization algorithm is presented which allows the stability problems to be solved. The implemented algorithm provides a measure of the accuracy of the solution achieved at each step. A numerical example is given, showing attractive features of the algorithm from the point of view of computational burden and convergence behavior