Finite-dimensional adaptive observers applied to distributed parameter systems

The application of finite-dimensional adaptive observers to distributed parameter systems is addressed. Ultimate boundedness of the parameter and state errors are proved in the case of residuals which have finite energy over a finite time interval, provided the plant input is definitely exciting. In the absence of definite excitation, an error growth rate of proportional to t^1/2 is proved. The results are obtained without assuming plant stability or input boundedness