Zero dynamics modeling and boundary feedback design for parabolic systems

Zero dynamics modeling and boundary feedback design for parabolic systems

In this work the authors introduce a notion of zero dynamics for distributed parameter systems governed by linear parabolic equations on bounded domains with controls implemented through first order linear boundary conditions. This notion is motivated by classical root-locus constructs from finite dimensional linear systems theory. In particular, for scalar proportional output feedback this not...

Discrete transparent boundary conditions for parabolic systems

In this work we construct and analyse transparent boundary conditions (TBCs) for general systems of parabolic equations. These TBCs are constructed for the fully discrete scheme (θ–method, finite differences), in order to maintain unconditional stability of the scheme and to avoid numerical reflections. The discrete transparent boundary conditions (DTBCs) are discrete convolutions in time and a...

Variational Modeling of Parabolic Free Boundary Problems

Backstepping design for parabolic systems with in-domain actuation and Robin boundary conditions

State feedback design for linear parabolic systems with in-domain actuation and general Robin boundary conditions is considered. To this end the system is shown to be state equivalent to a boundary controlled system. By means of the well established backstepping transformation this latter system is feedback equivalent to a stable parabolic equation. Within the contribution previous results conc...

Parabolic Systems with Coupled Boundary Conditions

We consider elliptic operators with operator-valued coefficients and discuss the associated parabolic problems. The unknowns are functions with values in a Hilbert space W . The system is equipped with a general class of coupled boundary conditions of the form f|∂Ω ∈ Y and ∂f ∂ν ∈ Y⊥, where Y is a closed subspace of L(∂Ω;W ). We discuss well-posedness and further qualitative properties, systema...