Bifurcation and Topology of Equilibrium Sets for Nonlinear Discrete Time Control Systems

Harmzi, Boumédiene; Barbot, Jean–Pierre; Kang, Wei

doi:10.1016/s1474-6670(17)40306-5

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2004

2023

Publication Types

Select...

Other3

Article3

Relationship

Self Cite0

Independent6

Authors

Journals

Cited by 8 publications

(1 citation statement)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Stabilization of systems with uncontrollable linearization, in continuous and discrete-time, were studied in [3], [4], [6], [7], [8], [13], [14], a complete description of symmetries around equilibrium [17], [21], and a characterization of systems equivalent to feedforward forms obtained in [19], [20].…”

Section: Introductionmentioning

confidence: 99%

Canonical forms for nonlinear discrete time control systems

Tall¹

2011

IEEE Conference on Decision and Control and European Control Conference

View full text Add to dashboard Cite

In this paper we provide a canonical form for discrete-time control systems whose linear approximation around an equilibrium is controllable and prove that two systems are feedback equivalent if and only if their canonical forms coincide. This is a nice generalization of results obtained for continuous time control systems. We also compute the homogeneous invariants under the action of a homogeneous feedback group. Consequently, as for the continuous systems, we deduce that the discrete time systems in consideration do not admit nontrivial symmetries, i.e., a map preserving the dynamics.

show abstract