New insights on the analysis of nonlinear time-delay systems

We present recent advances towards an algebraic framework for the analysis and control of nonlinear systems with delays. These results are applied to obtain results regarding the notion of integrability. Finally, we apply these results to obtain a constructive characterization of the equivalence of a given system to the so-called triangular form.

[1]  Claude H. Moog,et al.  Disturbance Decoupling for Time-Delay Nonlinear Systems: Dynamic Approach 1 , 1998 .

[2]  Choquet Bruhat,et al.  Analysis, Manifolds and Physics , 1977 .

[3]  C. Moog,et al.  A linear algebraic framework for dynamic feedback linearization , 1995, IEEE Trans. Autom. Control..

[4]  Toshiki Oguchi,et al.  Input-output linearization of retarded nonlinear systems by an extended Lie derivative , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[5]  John L. Casti,et al.  Introduction to the theory and application of differential equations with deviating arguments , 1973 .

[6]  H. Nijmeijer,et al.  Triangular Forms, Local Controllability and Stabilizability of Single-Input Nonlinear Systems , 1996 .

[7]  C. Moog,et al.  Triangular forms for nonlinear time-delay systems , 2001 .

[8]  Anna Maria Perdon,et al.  The Disturbance Decoupling Problem for Systems Over a Ring , 1995 .

[9]  Luis Alejandro Marquez-Martinez.  Analyse et commande de systèmes non linéaires à retards , 2000 .

[10]  L. A. Marquez-Martinez,et al.  New results on the analysis and control of nonlinear time-delay systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[11]  Alfredo Germani,et al.  Linearization and decoupling of nonlinear delay systems , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[12]  Xiaohua Xia,et al.  Analysis of nonlinear time-delay systems using modules over non-commutative rings , 2002, Autom..

[13]  Martín Velasco-Villa,et al.  The disturbance decoupling problem for time-delay nonlinear systems , 2000, IEEE Trans. Autom. Control..

[14]  Luis Alejandro Marquez-Martinez.  Note sur l'accessibilité des systèmes non linéaires à retards , 1999 .

[15]  Martín Velasco-Villa,et al.  The structure of nonlinear time delay systems , 2000, Kybernetika.

[16]  A. Arapostathis,et al.  Linearization of discrete-time systems , 1987 .

[17]  S. Bhat.  Controllability of Nonlinear Systems , 2022 .

[18]  B. Jakubczyk.  Feedback linearization of discrete-time systems , 1987 .

[19]  Eduardo Sontag,et al.  Controllability of Nonlinear Discrete-Time Systems: A Lie-Algebraic Approach , 1990, SIAM Journal on Control and Optimization.

[20]  Louis R. Hunt,et al.  Design for Multi-Input Nonlinear Systems , 1982 .