Regulation transients in DT-LPV systems: ℓ2-optimal approach via Hamiltonian system structural invariant subspaces

This work introduces an lscr
₂
-optimal approach for minimizing the regulation transients in discrete-time, linear systems subject to instantaneous, wide, a-priori-known parameter variations. The theoretical bases are twofold. A geometric interpretation, specifically aimed at discrete-time linear systems, of the multivariable autonomous regulator problem is required to define the ideal state trajectories, corresponding to the zero- error, steady-state conditions. A geometric characterization of the structural invariant subspaces of the singular Hamiltonian system associated to the optimal control problem is used to derive the actual state trajectories, corresponding to the minimal lscr
₂
-norm of the tracking error caused by parameter variations, given that the regulated system state cannot arbitrarily be imposed at the switching times. Since the proposed approach applies on the rather extensive conditions which guarantee solvability of a set of multivariable autonomous regulator problems as well as solvability of a set of optimal control problems, it is a valid option whenever the more restrictive conditions demanded to achieve perfect elimination of regulation transients are not satisfied.