Efficient computation of a guaranteed lower bound on the robust stability margin for a class of uncertain systems

Sufficient conditions for the robust stability of a class of uncertain syst ems, with several different assumptions on the structure and nature of the uncertainties, can be derived in a unified manner in the framework of integ ral quadratic constraints, These sufficient conditions, in turn, can be use d to derive lower bounds on the robust stability margin for such systems. T he lower bound is typically computed with a bisection scheme, with each ite ration requiring the solution of a linear matrix inequality feasibility pro blem. We show how this bisection can be avoided altogether by reformulating the lower bound computation problem as a single generalized eigenvalue min imization problem, which can be solved very efficiently using standard algo rithms. We illustrate this with several important, commonly encountered spe cial cases: diagonal, nonlinear uncertainties: diagonal, memoryless, time-i nvariant sector-bounded ("Popov") uncertainties; structured dynamic uncerta inties; and structured parametric uncertainties. We also present a numerica l example that demonstrates the computational savings that can be obtained with our approach.