Exponential Stability Of Linear Distributed Parameter Systems

The distributed parameter systems with boundary control or locally distributed control has attracted much attention in recent years (see,e.g. [19, 65]). In this thesis we concentrate on the following problems:1. The analyticity and the exponential stability for the thennoelastic plate with dynamical boundary conditions;2. The exponential stability for the viscoelastic plate with dynamical boundary conditions;3. The exponential stability for a system of elasticity with Dirichlet boundary feedback;4. The well-posedness and admissible stabilizability for Pritchard-Salamon systems.One of the main techniques we use is the frequency method. Falun Huang([52]) introduced the equivalent conditions of the spectrum determined growth assumption. Later Huang's result was used to prove the exponential stability for the distributed parameter systerns([92, 100]). We combine the frequency method with the techniques for partial differential equations, and induce the multiplier technique to get our exponential stability results.Pritchard-Salamon systems is a subset of infinite-dimensional linear systems with unbounded input arid output. In the last chapter of this thesis we obtain a characterization of generator of the perturbation semigroup for Pritchard-Salamon systems. So from this we establish that the "smooth condition" is unnecessary in the constructiveargument for Pritchard-Salamon systems. We also give a characterization of admissible stabiliz ability for Pritchard-Salamon systems by using the critical spectrum introduced recently.