D. Normand-Cyrot

Minimum-phase nonlinear discrete-time systems and feedback stabilization

In this paper, following ideas recently developed for a class of continuous systems, we introduce the notion of zero dynamics and minimum phase for discrete time nonlinear systems. On this basis, sufficient conditions are given for state feedback stabilization and full linearization via dynamic compensation. Relations with other properties of the system are also investigated.

Zero dynamics of sampled nonlinear systems

Abstract The behaviour of the zero dynamics of a discrete-time system obtained when sampling a continuous time nonlinear system is studied. We give a result which generalizes the known behaviour of the zeros of a sampled linear system for small time intervals.

An introduction to motion planning under multirate digital control

The authors propose digital control methods for steering real analytic controllable systems between arbitrary state configurations. The main idea is to achieve a multirate sampled procedure to perform motions in all the directions of controllability under piecewise constant controls. When it is applied to non-holonomic control systems without drift, the procedure simplifies. In particular, it results in exact steering on chained systems recently introduced in the motion planning literature. A classical example is reported.<<ETX>>

On the sampling of a linear analytic control system

In the present work we characterize the discrete time system which reproduces exactly the evolutions in the state of a given vector input linear analytic continuous time system driven by inputs which are constant on time intervals of fixed amplitude. This is achieved by comparing the Volterra series associated respectively to the sampled and continuous input state functionals. Moreover we give a compact Lie formula for the solution of a parametrized nonlinear differential equation which enables to characterize the nonlinear difference equation which solves the problem in terms of formal Lie series. On these bases, it becomes very natural to introduce a notion of approximated sampling of main efficiency in practical situations for computing purpose.

Issues on Nonlinear Digital Control

The purpose of this work is to show the real need to motivate theoretical research in nonlinear digital control not only for solving control problems which are specific to the context, but also for giving the intuition of new control methodologies. Digital control methods can, indeed, be used either for the design of piecewice constant feedback strategies or for the design of discontinuous and hybrid controllers.

On the observer design in discrete-time

Abstract The paper deals with the equivalence, under coordinates change and output transformation, of a discrete-time nonlinear system to observer canonical forms. Necessary and sufficient conditions for local equivalence to these forms are given.

Asymptotic properties of incrementally stable systems

It is shown that incremental stability of an input-output operator ensures asymptotic stability of any equilibrium pair (x/sub e/, u/sub e/) of its state representation if suitable minimality assumptions hold.

On regulation under sampling

The paper deals with linear and nonlinear regulation under sampling. It is shown that digital solutions exist under assumptions which are closely related to the existence of robust solutions to the continuous problem. Approximated solutions are computed starting from the continuous ones.

Advanced tools for nonlinear sampled-data systems' analysis and control

It is shown that the formalism of asymptotic series expansions recently developed by the authors for computing the solutions of non autonomous differential equations, can be profitably employed to obtain the equivalent model to a nonlinear continuous system under generalized sampling procedures. Tools and insights for the design of sampled-data control systems are derived.

Nonlinear regulation for a class of discrete-time systems

Abstract This paper deals with nonlinear discrete-time regulation for multi-input, multi-output plants. Conditions involving solvability of nonlinear transcendental equations are set. Following the approach recently developed by Isidori and Byrnes (1990) for continuous time systems, the existence of solutions to the posed problem is proved by investigating the properties of the zero dynamics. Finally a condition is given for the existence of an arbitrary approximation of the nonlinear solution.