Output regulation in switched linear parameter varying systems with preview: The continuous-time case

This paper deals with the problem of perfect elimination of the transients of the regulated output caused by parameter variations, in continuous-time multivariable linear systems. Parameter changes are assumed to be instantaneous and known in advance within a finite time horizon. The continuous-time case needs separate investigation from the discrete-time case, that has recently been solved both in the exact context and in the ℓ₂-optimal context. In fact, the continuous-time solution of the exact problem cannot be found through a plain conversion from continuous to discrete, since discretizations do not generically preserve the geometric properties of the set of switched systems playing a key role in the specific synthesis procedure. Moreover, the continuous-time exact solution cannot straightforwardly be retrieved as the zero-cost solution of the corresponding optimization problem, since the latter turns out to be a singular problem in general, due to the structure of the systems involved. In the light of these considerations, geometric conditions for the continuous-time problem solvability are proved and a complete design procedure is presented.