Stabilization for a coupled PDE-ODE control system

DOI10.1016/j.jfranklin.2011.06.008zbMath1231.93095OpenAlexW2106223553MaRDI QIDQ658616

Chengkang Xie, Shu-Xia Tang

Publication date: 13 January 2012

Published in: Journal of the Franklin Institute (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfranklin.2011.06.008

zbMATH Keywords

exponential stabilitycoupled PDE-ODE control systeminvertible integral transformationstate feedback boundary controller

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Stabilization of systems by feedback (93D15) Observability (93B07) Control/observation systems governed by ordinary differential equations (93C15)

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Cites Work

• Adaptive stabilization of linear and nonlinear plants in the presence of large and arbitrarily fast variations of the parameters
• Control of PDE-ODE cascades with Neumann interconnections
• Numerical issues in backstepping control: sensitivity and parameter tuning
• Exponential stability and stabilization of a class of uncertain linear time-delay systems
• Finite-time stabilization of nonlinear dynamical systems via control vector Lyapunov functions
• Delay-independent stabilization of linear systems with time-varying delayed state and uncertainties
• Compensating actuator and sensor dynamics governed by diffusion PDEs
• Delay compensation for nonlinear, adaptive, and PDE systems
• Control, observation and polynomial decay for a coupled heat-wave system
• Polynomial decay and control of a 1-d model for fluid-structure interaction.
• Polynomial decay and control of a 1D hyperbolic-parabolic coupled system
• Backstepping observers for a class of parabolic PDEs
• Backstepping boundary control for first-order hyperbolic PDEs and application to systems with actuator and sensor delays
• Compensating a String PDE in the Actuation or Sensing Path of an Unstable ODE

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