Systems with uncertain parameters — time‐variations with bounded derivatives

It is shown how derivative bounds on uncertain time-varying parameters can be exploited in robustness analysis of linear systems. A new stability criterion is derived, based on integral quadratic constraints (IQCs) in the frequency domain. The new stability criterion interpolates between well-known stability results. As the derivative bounds tend to zero, the new criterion turns into the usual upper bound for the structured singular value. The stability analysis, which involves a search for suitable multipliers, can be formulated as a convex optimization problem in terms of linear matrix inequalities.