Linearization Of Discrete-time Systems Research Articles

Linearization of discrete-time systems by exogenous dynamic feedback

It is shown that a discrete-time system may be linearizable by exogenous dynamic feedback, even if it cannot be linearized by endogenous feedback. This property is completely unexpected and constitutes a fundamental difference with respect to the continuous-time case. The notion of exogenous linearizing output is introduced. It is shown that existence of an exogenous linearizing output is a sufficient condition for dynamic linearizability. Necessary and sufficient conditions for the existence of an exogenous linearizing output are provided. The results of the paper are obtained using transformal operator matrices. The properties of such operators are studied. The theory is applied to the exact discrete-time model of a mobile robot, showing that the above-mentioned property concerns not only academic examples, but also physical systems.

Linearization of discrete-time systems via restricted dynamic feedback

We extend the results from a previous paper of ours to multiple-input systems, and utilize these to obtain necessary and sufficient conditions for the linearization of discrete-time nonlinear systems via restricted dynamic feedback. We observe that for discrete-time nonlinear systems, the bound on the number of delays (or integrators) needed to synthesize the linearizing dynamic feedback differs from the continuous-time analogue.

Approximate I/O Feedback Linearization of Discrete-Time Non-Linear Systems via Virtual Input Direct Design

The design of linearizing compensators via output-feedback for discrete-time non-linear plants, using I/O measurements only, is typically performed in an indirect way by identifying first a non-linear model of the plant, and resorting then to a suitable model-based design technique. In this paper we propose the use of a new method, based on a virtual input direct design (VID 2) approach. The main feature of such a method is to carry the control design into a standard non-linear mapping approximation problem, thus avoiding any preliminary plant-identification phase. As compared with the existing methods, the new one requires less computational effort, while taking full advantage of the non-linear approximation software tools already available. In this paper, the new method is described, and some theoretical results are given, concerning the I/O linearization of discrete-time systems via dynamic output feedback.

Linearization of Discrete-Time Systems

The algebraic formalism developed in this paper unifies the study of the accessibility problem and various notions of feedback linearizability for discrete-time nonlinear systems. The accessibility problem for nonlinear discrete-time systems is shown to be easy to tackle by means of standard linear algebraic tools, whereas this is not the case for nonlinear continuous-time systems, in which case the most suitable approach is provided by differential geometry. The feedback linearization problem for discrete-time systems is recasted through the language of differential forms. In the event that a system is not feedback linearizable, the largest feedback linearizable subsystem is characterized within the same formalism using the notion of derived flag of a Pfaffian system. A discrete-time system may be linearizable by dynamic state feedback, though it is not linearizable by static state feedback. Necessary and sufficient conditions are given for the existence of a so-called linearizing output, which in turn is a sufficient condition for dynamic state feedback linearizability.

Nonsmooth stabilizability and feedback linearization of discrete-time nonlinear systems

We consider the problem of stabilizing a discrete-time nonlinear system using a feedback which is not necessarily smooth. A sufficient condition for global dynamical stabilizability of single-input triangular systems is given. We obtain conditions expressed in terms of distributions for the nonsmooth feedback triangularization and linearization of discrete-time systems. Relations between stabilization and linearization of discrete-time systems are given.

Nonsmooth stabilizability and feedback linearization of discrete‐time nonlinear systems

We consider the problem of stabilizing a discrete-time nonlinear system using a feedback which is not necessarily smooth. A sufficient condition for global dynamical stabilizability of single-input triangular systems is given. We obtain conditions expressed in terms of distributions for the nonsmooth feedback triangularization and linearization of discrete-time systems. Relations between stabilization and linearization of discrete-time systems are given.

Linearization of discrete-time systems

Abstract We characterize the equivalence of single-input single-output discrete-time nonlinear systems to linear ones, via a state-coordinate change and with or without feedback. Four cases are distinguished by allowing or disallowing feedback as well as by including the output map or not; the interdependence of these problems is analyzed. An important feature that distinguishes these discrete-time problems from the corresponding problem in continuous-time is that the state-coordinate transformation is here directly computable as a higher composition of the system and output maps. Finally, certain connections are made with the continuous-time case.