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- Klaus Schmidt, Ece Guran Schmidt
- IEEE Trans. Vehicular Technology
- 2009

Let α be an action of Z d by continuous automorphisms of a compact abelian group X. A point x in X is called homoclinic for α if α n x → 0X as n → ∞. We study the set ∆α(X) of homoclinic points for α, which is a subgroup of X. If α is expansive then ∆α(X) is at most countable. Our main results are that if α is expansive, then (1) ∆α(x) is nontrivial if and… (More)

- Anatole Katok, Svetlana Katok, Klaus Schmidt
- 2000

We show that for certain classes of actions of Z d ; d 2, by automorphisms of the torus any measurable conjugacy has to be aane, hence measurable conjugacy implies algebraic conju-gacy; similarly any measurable factor is algebraic, and algebraic and aane centralizers provide invariants of measurable conjugacy. Using the algebraic machinery of dual modules… (More)

- Klaus Schmidt
- 1999

Let α be an expansive automorphisms of compact connected abelian group X whose dual groupˆX is cyclic w.r.t. α (i.e. ˆ X is generated by {χ · α n : n ∈ Z} for some χ ∈ ˆ X). Then there exists a canonical group homomorphism ξ from the space ∞ (Z, Z) of all bounded two-sided sequences of integers onto X such that ξ · σ = α · ξ, where σ is the shift on ∞ (Z,… (More)

- KLAUS SCHMIDT
- 1995

We prove that certain Gibbs measures on subshifts of finite type are nonsingular and ergodic for certain countable equivalence relations, including the orbit relation of the adic transformation (the same as equality after a permutation of finitely many coordinates). The relations we consider are defined by cocycles taking values in groups, including some… (More)

- Klaus Schmidt
- Systems & Control Letters
- 2010

In this paper, we introduce the idea of abstraction-based diagnosability for large-scale composed discrete event systems that consist of multiple subsystems. To this end, we determine sufficient conditions such that diagnosability of the original system follows from diagnosability of an abstracted system model on a smaller state space. In addition, we prove… (More)

Let d ≥ 1, and let α be an expansive Z d-action by continuous automorphisms of a compact abelian group X with completely positive entropy. Then the group ∆α(X) of homoclinic points of α is countable and dense in X, and the restriction of α to the α-invariant subgroup ∆α(X) is a Z d-action by automorphisms of ∆α(X). By duality, there exists a Z d-action α *… (More)

- Klaus Schmidt
- Automatica
- 2010

In this paper, we investigate the verification of codiagnosability for discrete event systems (DES). That is, it is desired to ascertain if the occurrence of system faults can be detected based on the information of multiple local sites that partially observe the overall DES. As an improvement of existing codiagnosability tests that resort to the original… (More)

- Ece Guran Schmidt, Klaus Schmidt
- IEEE Trans. Vehicular Technology
- 2009

—The FlexRay communication protocol is expected to be the de-facto standard for high-speed in-vehicle communication. In this paper, we formally investigate the scheduling problem for the dynamic segment of FlexRay. We take the bounds on the generation times and the timing requirements of the signals into consideration to propose a reservation based… (More)

- KLAUS SCHMIDT
- 1993

We prove that every mixing Z d-action by automor-phisms of a compact, connected, abelian group is mixing of all orders.