H2 and H∞ e-guaranteed cost computation of uncertain linear systems

An approach to compute the H₂- or H_infin-guaranteed costs with any prescribed accuracy is presented. The proposed approach can be applied to uncertain state-space models of linear time-invariant systems, where the system matrices depend on uncertain parameters or vary in a polytopic domain of the space of matrices. The developed approach is based on a new implementation of the branch-and-bound algorithm with the upper-bound functions based on linear matrix inequality (LMI) characterisations. The branch operation is based on a new subdivision technique that can be applied to any kind of polytope shape, not restricted to the hyper-rectangle case. When applied alone, the LMI-based analysis formulations can fail to compute the guaranteed costs, or they can present conservative results. Examples are presented to illustrate that the proposed analysis approach overcomes the problems faced with LMI-based formulations with reasonable computational time.