Systems with uncertain parameters-time-variations with bounded derivatives

In this paper, 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 in the frequency domain. The new stability criterion interpolates between well known robust stability results, which are obtained in the limit. 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