Tracking problems with H∞ disturbance attenuation for sampled-data systems via jump system approach

This paper is concerned with finite-horizon H_infin tracking problems for sampled-data systems. A jump system approach is employed to analyze sampled-data systems because a jump system represents a wide class of systems, including not only continuous-time and discrete-time systems, but also sampled-data systems. Three tracking problems are considered, depending on whether the reference signals are perfectly known in advance, measured on-line or previewed in fixed interval of time ahead. No a priori knowledge of a dynamic model for the reference signal is assumed. A game theory approach is taken to solve the problems where for the specific reference signals the controllers play against nature which can choose any initial state and any bounded energy disturbance input and measurement noise. Necessary and sufficient conditions for the existence of a saddle-point equilibrium are determined, and H_infin tracking controllers for both the cases of state and output feedbacks are obtained