H∞ Guaranteed Cost Computation for Uncertain Time-Delay Systems

This paper presents a less conservative approach to compute, with any prescribed accuracy, the H∞ guaranteed cost of time-delay continuous-time linear time-invariant systems subjected to polytopic uncertainties. The proposed analysis approach is based on a branch-and-bound algorithm that incorporates a recent LMI-based analysis formulation and a new polytope partition strategy. In the branch-and-bound algorithm, the upper bound function is defined as the worst case guaranteed H∞ disturbance attenuation level computed for the subpolytopes achieved with successive partitions of the polytope which describes the uncertainty domain. The lower bound function is defined as the worst case H∞ norm computed in the polytope and subpolytope vertices. The difference between the upper and lower bound functions converges to zero as the initial polytope is split into smaller subpolytopes resulting in the H∞ guaranteed cost for the whole initial polytope with the required accuracy. It is also presented an algorithm to implement a d−dimensional simplex subdivision technique to be used in the branch-and-bound algorithm.