Analysis of Nonlinear Discrete-Time Control Systems based on Lie-Groups

This contribution is concerned with the observability and accessibility analysis of nonlinear explicit discrete-time control systems. The presented approach is fundamental based on the fact that the geometric interpretation known from the analysis of continuous-time systems based on Lie groups is also appropriate in the discrete-time case. It is shown that by investigation of invariants of Lie groups acting on the solution of the system it is possible to state conditions for local observability and accessibility without calculating the solution. These methods provide tests which can be done by computer algebra.