Driven dynamics of time-varying linear systems

Motivated by applications to automatic control of aircraft, we consider the problem of output tracking for time-varying linear systems. The signals to be tracked are bounded on (-∞, ∞), and our goal is to compute bounded controls and bounded state trajectories that result in the desired tracking. A convolution integral representation for the desired solution is given in the literature, and we show that certain integrability assumptions can be eliminated from the associated results. Despite the fact that our system is time varying and our signals do not necessarily have Fourier transforms in the classical sense, we show that computations can be carried out using “generalized” Fourier transforms. We also consider an output tracking problem in which the driven dynamical equation is an ordinary differential equation