# Moduli and canonical forms for linear dynamical systems II: The topological case

@article{Hazewinkel2005ModuliAC, title={Moduli and canonical forms for linear dynamical systems II: The topological case}, author={M. Hazewinkel}, journal={Mathematical systems theory}, year={2005}, volume={10}, pages={363-385} }

AbstractIn this paper we study real linear dynamical systems
$$\dot x = Fx + Gu,y = Hx,x \in R^n $$
= state space,u ∈Rm = input space,y ∈Rp = output space, under the equivalence relation induced by base change in state space; or in other words we study triples of matrices with real coefficients (F, G, H) of sizesn × n, n × m, p × n respectively, under the action(F, G, H.) →(TFT−1,TG, HT−1) ofGLn(R), the group of invertible realn × n matrices. One of the central questions studied is: “do there… CONTINUE READING

#### Topics from this paper

21 Citations

Bundle Reduction and the Alignment Distance on Spaces of State-Space LTI Systems

- Mathematics, Computer Science
- IEEE Transactions on Automatic Control
- 2017

4 Highly Influenced- PDF

Topology of the moduli space for reachable linear dynamical systems: The complex case

- Mathematics, Computer Science
- Mathematical systems theory
- 2005

15

A continuous canonical form for static output feedback in linear system

- Mathematics
- 2012 12th International Conference on Control, Automation and Systems
- 2012

Differential geometry of a parametric family of invertible linear systems—Riemannian metric, dual affine connections, and divergence

- Mathematics, Computer Science
- Mathematical systems theory
- 2005

54

Riemannian optimal system identification method of linear continuous-time systems with symmetry

- Mathematics
- 2018

Highly Influenced

Riemannian Optimal Identification Method for Linear Systems With Symmetric Positive-Definite Matrix

- Mathematics, Computer Science
- IEEE Transactions on Automatic Control
- 2020

1- PDF

Global structure of families of multivariable linear systems with an application to identification

- Mathematics, Computer Science
- Mathematical systems theory
- 2005

12

#### References

SHOWING 1-10 OF 27 REFERENCES

On Invariants, Canonical Forms and Moduli for Linear, Constant, Finite Dimensional, Dynamical Systems

- Mathematics
- 1976

129- PDF

Moduli and canonical forms for linear dynamical systems III : the algebraic-geometric case

- Mathematics
- 1977

35

Canonical Forms and Moduli for Linear, Constant, Finite Dimensional, Dynamical Systems

- Proc. CNR-CISM symposium on "Algebraic System Theory
- 1975

(R), x-> cf>ab(f(x)) fa: V~ x R"-> V~ x R

) denote the set of isomorphism classes of completely reachable families of linear systems (of dimensions (n, m, p)) over S. Now let/: S'-+ S be a continuous map

) iflab(s)aa(s)R(Fa,., Ga,)= R(F,(f(s)), G0 (f(s)))iJ 1 R(F)f(s))

11) then mean that F

- · p(R) be the n-vectorbundle obtained by glueing together the E, by means of the $

8) implies that R(Fa,s• Ga.sl. has nonzero determinant)