Output regulation for a class of linear hybrid systems. Part 1: trajectory generation

In this paper the problem of generating zero error steady-state responses is addressed for a class of hybrid linear systems whose jumps are determined by time only. The procedure for the design of an automatic device generating the steady-state response and input is described. Once such device and a compensator ensuring incremental stability (see the companion paper) are available, the classical output regulation problem for the same class of hybrid linear systems can be immediately solved. Compared with previously available results, no assumption is needed on the plant about minimum phaseness, relative degree or squareness (same number of inputs and outputs). The key role of the zero dynamics and of the additional inputs (when the plant is fat) is highlighted.