Abstract
This paper is concerned with the stabilization problem of semilinear distributed parameter systems with unbounded output operators. Especially, the output operators are assumed to be Aγ-bounded. For example, the semilinear diffusion system with boundary control and boundary observation is formulated as a semilinear evolution equation with Aγ-bounded output operator in a Hilbert space. Balas has shown that a nonlinear finite-dimensional controller with a nonlinear residual mode filter can produce closedloop stability with a given semilinear distributed parameter system with bounded input and output operators. However, he does not discuss on the systems with unbounded input operators or unbounded output operators.
In this paper, we show that Balas-type of nonlinear controller is also effective for the semilinear distributed parameter system with Aγ-bounded output operator. Then, we can give the decay rate of the closed-loop system by using the modified Gronwall's inequality. Moreover, it is shown that the use of nonlinear controller in the above brings more preferable result than the use of linear controller with a usual residual mode filter.
