In the last three decades, linear infinite dimensional systems theory has been extensively studied. The basic concepts in linear finite-dimensional dynamical systems theory, such as transfer functions, state space representation, controllability, observability, and stability, have been successfully extended to the study of linear infinite-dimensional systems. Given the inherent nonlinear behaviours of practical science and engineering systems, this project aims to extend the nonlinear system frequency domain theories and methods for finite dimensional systems to the infinite-dimensional case. The project will focus on the further development of the frequency domain theory and methods of nonlinear infinite-dimensional systems, or be concerned with the application of the novel techniques that have been proposed at Sheffield to tackle different science and engineering problems such as turbulence, reaction-diffusion, and health monitoring of engineering structures.
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