Analysis and Nonlinear Control of Implicit Discrete-time Dynamic Systems

This contribution is concerned with the observability and accessibility analysis as well as the nonlinear control of discrete-time dynamic systems described by implicit difference equations. It is the fundamental observation that the geometric interpretation of the analysis based on Lie groups for implicit continuous-time dynamic systems is also appropriate in the discrete-time case. By investigation of invariant functions for Lie groups acting on the solution of the system a formal method to state conditions for local observability and accessibility is obtained. These methods provide tests which can be done by computer algebra. Furthermore, a nonlinear discrete-time control design approach for input-to-state linearizable continuous-time control systems is presented.