Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions

1978/10/01 by David L. Russell · 30 citations
Engineering · Mathematics · Physics and Astronomy · #Stability and Controllability of Differential Equations #Numerical methods for differential equations #Model Reduction and Neural Networks

paper · doi:10.1137/1020095

Abstract

This paper is an assessment of the current state of controllability and observability theories for linear partial differential equations, summarizing existing results and indicating open problems in the area. (Author)

Citations

• Nonharmonic Fourier series in the control theory of distributed parameter systems

Cited by

• Exact Controllability, Stabilization and Perturbations for Distributed Systems
• Simultaneous controllability of wave sound propagations
• Theorical and Numerical Analysis of the Rapid Pointwise Stabilization of Coupled String-Beam Systems
• Stabilization of the wave equation with external force
• Two-point boundary value problems and exact controllability for several kinds of linear and nonlinear wave equations
• Stabilizability with bounded feedback for analytic linear control systems
• Input delayed boundary control of a heat-heat cascade
• Numerical boundary control of multi-dimensional discrete-velocity kinetic models
• Finite-dimensional observer-based boundary stabilization of\n reaction-diffusion equations with a either Dirichlet or Neumann boundary\n measurement
• A Harmonic Analysis Proof of the Boundary Observability Inequality for the Wave Equation and Visco-Elastic Equation
• Experimental Study of the HUM Control Operator for Linear Waves
• Null-controllability of linear hyperbolic systems in one dimensional\n space
• Finite Time Stabilization of Nonautonomous First Order Hyperbolic\n Systems
• Stabilization of infinite-dimensional linear control systems by POD reduced-order Riccati feedback
• Feedback stabilization of a 1D linear reaction-diffusion equation with\n delay boundary control
• Finite Codimensional Controllability, and Optimal Control Problems with Endpoint State Constraints
• Exact Controllability of Linear Stochastic Differential Equations and Related Problems
• An inverse problem for a hyperbolic system on a vector bundle and energy\n measurements
• Source Reconstruction and Stability via Boundary Control of Abstract Viscoelastic Systems
• On the controllability and Stabilization of the Benjamin Equation
• On the Observability Inequality of Coupled Wave Equations: the Case without Boundary
• Semiglobal exponential stabilization of nonautonomous semilinear parabolic-like systems
• A different look at controllability
• A Concise Introduction to Control Theory for Stochastic Partial Differential Equations
• Local exponential H² stabilization of a 2X2 quasilinear hyperbolic system using backstepping
• Memory-Type Null Controllability of Heat Equations with Delay Effects
• Boundary Output Feedback Stabilization of Reaction-Diffusion PDEs with Delayed Boundary Measurement
• Super-Resolution Off the Grid
• Observation of vibrating systems at different time instants
• Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary

Related

• A unified controllability/observability theory for some stochastic and deterministic partial differential equations
• The Consistency of Partial Observability for PDEs
• Multitime controlled linear PDE systems
• Quadratic obstructions to controllability: from ODEs to PDEs
• Effect of linear lumping on controllability and observability