A Constraint Propagation Algorithm for Determining the Stability Margin of Linear Parameter Circuits and Systems

The paper addresses the stability margin assessment for linear systems under interval parameter uncertainties. The original robust stability problem is initially transformed into an equivalent problem of estimating the eigenvalues ranges of matrices whose elements are non-linear functions of independent interval parameters. A new algorithm for finding the exact value of stability margin (within error bounds) is suggested. It is based on the use of the inner and outer bounds on the right ends of the eigenvalue considered in order to determine as a narrow initial uncertainty region as possible. Then the constraint propagation approach is applied. It consists of two steps. First, one sweep of constraint propagation, relative to the interval components of the eigenvalue – eigenvector pair, is carried out, keeping the parameter intervals fixed. Next, a second sweep of constraint propagation, relative to the components of the interval parameters, is applied, keeping the reduced intervals of the eigenvalue – eigenvector pair fixed. A numerical example, illustrating the applicability of the algorithm suggested, is solved at the end.