An algebraic approach to boundary stabilization for parabolic systems with Dirichlet boundaries

Stabilization of linear parabolic boundary control systems is studied. While the system consists of a pair of standard linear differential operators (L,τ) of the Dirichlet type, it generally admits no Riesz basis associated with them. In this sense the system has enough generality as a prototype of general systems. A difficulty arises when we apply the existing procedures, via fractional powers of the associated elliptic operator, to our problem. The paper proposes a new algebraic approach to stabilization which has a substantial application to a variety of boundary control systems including dynamics arising in problems of robotics