Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities

摘要

Using Hermite's formulation of polynomial stability conditions, static outputfeedback (SOF) controller design can be formulated as a polynomial matrixinequality (PMI), a (generally nonconvex) nonlinear semidefinite programmingproblem that can be solved (locally) with PENNON, an implementation of apenalty method. Typically, Hermite SOF PMI problems are badly scaled andexperiments reveal that this has a negative impact on the overall performanceof the solver. In this note we recall the algebraic interpretation of Hermite'squadratic form as a particular Bezoutian and we use results on polynomialinterpolation to express the Hermite PMI in a Lagrange polynomial basis, as analternative to the conventional power basis. Numerical experiments on benchmarkproblem instances show the substantial improvement brought by the approach, interms of problem scaling, number of iterations and convergence behavior ofPENNON.