Journal ArticleDOI
Feedback stabilization of a class of distributed systems and construction of a state estimator
Yoshiyuki Sakawa,T. Matsushita +1 more
Reads0
Chats0
TLDR
In this paper, it is proved that, when a controller (an observation) can be arbitrarily constructed, observability (controllability) of the system is necessary and sufficient for stabilizing the system so that it has an arbitrarily large damping constant.Abstract:
In this paper, we study feedback stabilization of a class of distributed systems governed by partial differential equations of parabolic type and its application to constructing a state estimator for asymptotic state identification. It is proved that, when a controller (an observation) can be arbitrarily constructed, observability (controllability) of the system is necessary and sufficient for stabilizing the system so that it has an arbitrarily large damping constant. As an application of this result, it is shown that a state estimator can be constructed, the output of which approaches asymptotically the real state of the system with an arbitrary convergence rate.read more
Citations
More filters
Journal ArticleDOI
Robust multivariable PI-controller for infinite dimensional systems
TL;DR: In this paper, a robust multivariable PI-controller was proposed for a class of distributed parameter systems. But it is not shown that the controller can be tuned on the basis of step responses without exact knowledge of the system's parameters.
Journal ArticleDOI
Finite-dimensional compensator design for parabolic distributed systems with point sensors and boundary input
TL;DR: In this paper, a modal approach utilizing known finite-dimensional algorithms for observer and stabilizer design is proposed for a large class of parabolic distributed systems, where the observer is constructed from observations taken from point or averaging sensors and the compensator is a feedback of this observer and can be a "distributed" or "boundary" implementation.
Book ChapterDOI
Feedback control of linear diffusion processes
TL;DR: In this article, the authors considered the class of diffusion processes described by the generalized heat equation and obtained a practical feedback controller for N system modes, where the remaining process modes are effected by the controller and this control spillover is shown to reduce the desired system response time by a predictable amount.
Journal ArticleDOI
Finite dimensional compensators for parabolic distributed systems with unbounded control and observation
TL;DR: In this article, it was proved that for a class of parabolic distributed parameter systems with unbounded control and observation, there exists a finite dimensional compensator using dynamic output feedback.
Proceedings ArticleDOI
Observers for linear distributed-parameter systems: A survey
TL;DR: This paper surveys observers for first-order and second-order linear distributed-parameter systems based on their infinite-dimensional and finite-dimensional descriptions.
References
More filters
Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Journal ArticleDOI
Observers for multivariable systems
TL;DR: In this article, it was shown that the design of an observer for a system with M outputs can be reduced to the design for m separate observers for single-output subsystems.
Journal ArticleDOI
On pole assignment in multi-input controllable linear systems
TL;DR: In this paper, it was shown that controllability of an open-loop system is equivalent to the possibility of assigning an arbitrary set of poles to the transfer matrix of the closed loop system, formed by means of suitable linear feedback of the state.
Book
The theory of partial differential equations
TL;DR: In this article, Fourier series and Fourier transforms have been used to describe fundamental theory, evolution equations, and semi-linear hyperbolic equations, as well as a number of others.