Exact controllability of wave equations with variable coefficients coupled in parallel

Abstract

In this paper, we investigate exact controllability for coupled wave equations which have variable coefficients principal part. Observability inequality is obtained by using Riemannian geometry method and Carleman estimates. Furthermore, the exact controllability result is established with Dirichlet boundary controls when T>T0, where the lower bound T0 for the control time T is different from that obtained in the constant coefficient principal part case. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

A Note on the Controllability and Observability for Piecewise Linear Time‐varying Impulsive Systems

“…Hence, the study of systems with impulsive effects is of great importance . Since the controllability and observability have close connections to pole assignment, structural decomposition, and so on, they have played a central role throughout the history of modern control theory and engineering, see and the references therein.…”

Boundary controllability for the quasi-linear wave equations coupled in parallel

“…Stabilization and controllability for systems coupled by linear wave equations in parallel can be found in papers [19,15,20] and [18]. Such systems of the quasi-linear case have not been considered.…”

“…Controllability for coupled linear wave equations has been investigated by many authors, we refer the readers to [15][16][17][18][19][20], etc. There are few results in higher dimensions for nonlinear cases.…”

Well-posedness for a variable-coefficient wave equation with nonlinear damped acoustic boundary conditions

“…This is a new and powerful method to deal with variable coefficients. It was introduced by Yao [20] to deal with controllability for variable-coefficient waves, and has been widely used in the literature, for instance, see [21][22][23][24][25][26][27][28]. The classical analysis was originally successful in dealing with the constant-coefficient wave equations, but proved inadequate in treating variablecoefficient cases.…”