Robust control design of linear systems with polytopic time-varying uncertainty: An iterative SDP approach

This paper considers the nonlinear optimization problems arising in robust control synthesis for discrete linear systems with polytopic time-varying uncertainty. Here a linear objective function is minimized under nonlinear matrix-valued function constraints. An iterative semidefinite programming (SDP) method is used to this class of problems. The benefit of the new approach is that the sub-problems in the iterative SDP are all based on linear matrix inequalities (LMIs) and can be solved efficiently. Iterative SDP based algorithms are then proposed for the robust stabilization and optimal control problems, respectively. A numerical example is used to compare the SDP and LMI based design which shows that the SDP one is less conservative.