The central theme of the proposed research is the use of recent contributions in the representation of time-varying systems in the theory of robust controller design. This analysis will include the recently introduced W-transform, which is a generalization to time-varying systems of the well known Laplace transform, as well as other time-frequency analysis tools, such as the wavelet transform.
Part of the research proposed will develop a rigorous theory of poles and zeros for time-varying systems. This theory will then be used to consider the fundamental limits that exist in time-varying designs and the effect of the poles and zeros on the closed-loop performance of the system. This research will lead to research into filters that may be suitable for robust control design. Finally, we propose to develop the theory of time/frequency representation of these filters.
The research proposed here will bridge the gap between the optimal control theory of linear time-varying systems, and the means for designing effective controllers for these systems. It will have the additional benefit of unifying the powerful Hoo. control theory with the current advances being made in time-frequency representations of time-varying systems. Because of the interdisciplinary nature of this research - bringing together recent advances in signal processing into the control theory community - this research program will strengthen the connection between the two fields. This should help broaden the educational experience of the students involved in this research.
In addition to its use for the study of time-varying systems, the theory developed as part of this proposal should be useful for the control of systems where the time-variations are externally imposed, for example, in gain scheduled controlled systems, parameter varying systems, and hybrid systems.
