Luenberger boundary observer synthesis for Sturm–Liouville systems

Abstract

A static Luenberger observer of a system with Sturm–Liouville operator is synthesised with the aid of a boundary control formulation. To this aim, approximate observability, detectability and stability of the system is studied and design results are worked out for a typical biochemical case study.

Keywords:

• boundary control system
• observer synthesis
• Luenberger observer
• distributed parameter system
• Sturm–Liouville system

Notes

Notes

1. The semigroup is defined as in Definition 2.1.8, Chapter 2 of Curtain and Zwart (1995).

2. The definition of a Riesz spectral operator is found in Theorem 2.3.5 in Curtain and Zwart (1995).

3. Operator Q is said to be positive if ⟨Az, z⟩ > 0 for all nonzero z ∈ D(Q).

4. The growth bound of a semigroup T is given by

5. The definition of a growth bound ω₀ of a Riesz spectral operator is