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This work proposes a novel robust model predictive control (MPC) algorithmfor linear systems affected by dynamic model uncertainty and exogenousdisturbances. The uncertainty is modeled using a linear fractional perturbationstructure with a time-varying perturbation matrix, enabling the algorithm to beapplied to a large model class. The MPC controller constructs a state tube as asequence of parameterized ellipsoidal sets to bound the state trajectories ofthe system. The proposed approach results in a semidefinite program to besolved online, whose size scales linearly with the order of the system. Thedesign of the state tube is formulated as an offline optimization problem,which offers flexibility to impose desirable features such as robust invarianceon the terminal set. This contrasts with most existing tube MPC strategiesusing polytopic sets in the state tube, which are difficult to design and whosecomplexity grows combinatorially with the system order. The algorithmguarantees constraint satisfaction, recursive feasibility, and stability of theclosed loop. The advantages of the algorithm are demonstrated using twosimulation studies.

Scalable tube model predictive control of uncertain linear systems using ellipsoidal sets