A Classification of Nonlinear Systems Based on the Invariant Subdistribution Algorithm

• Maria Domenia Di Benedetto
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 29)

Abstract

Consider a nonlinear system of the form
$$\dot{x} = f(x) + \sum\limits_{{i = 1}}^m {{g_i}(x){u_i}} y = h(x)$$
(1.1)
with state x ∈ X Ì ℝn, input u ∈ ℝm and output y ∈ ℝP; f and g1,...,gm are analytic vector fields on X and h is an analytic function.

References

1. [1]
A.J. Krener: (Adf,g),(adf,g) and Locally (adf,g) Invariant and Controllability Distributions. SIAM J. Control and Optimization, 23, 523–549, (1985).
2. [2]
A. Isidori, A.J. Krener, C. Gori-Giorgi, S. Monaco: Nonlinear Decoupling via Feedback: A Differential-Geometric Approach IEEE Trans. Automat. Contr., Vol. AC-26, 331–345, (1981).
3. [3]
H. Nijmeijer, J.M. Schumacher: Zeros at Infinity for Affine Nonlinear Control Systems. IEEE Trans. Automat. Contr., Vol. AC-30, 566–573, (1985).
4. [4]
M.D. Di Benedetto, A. Isidori: The Matching of Nonlinear Models via Dynamic State Feedback. Proc. 23rd CDC, Las Vegas, (Dec. 1984), to appear on SIAM J. of Contr. and Optimization.Google Scholar
5. [5]
H. Nijmeijer: Right-invertibility for nonlinear control systems: a geometric approach. Memo. 484, Dept. Appl. Math., Twente University of Technology, (1984).Google Scholar
6. [6]
A. Isidori, A. Ruberti: On the Synthesis of Linear Input-Output Responses for Nonlinear Systems. Sys. Control Lett. 4, 17–22, (1984).
7. [7]
A. Isidori: Nonlinear Control Systems: an Introduction. Lect. Notes in Control and Information Science, Vol. 72, Springer-Verlag, (1985).
8. [8]
A. Isidori: Control of Nonlinear Systems via Dynamic State Feedback. Algebraic and Geometric Methods in Nonlinear Control Theory, M. Fliess and M. Hazewinkel eds., Reidel, Dordrecht, (1986). This volume.Google Scholar