| Deconvolution filtering problems in dynamic systems have wide applications in seismology, oil exploration, image restoration, fault detection, signal processing, communications, and equalization. This thesis aims at designing deconvolution filters with guaranteed energy-to-peak performance.;In Chapter 3, we study the l2 – l∞ IIR deconvolution filter design. The sufficient and necessary condition is derived to guarantee the l 2 – l∞ filtering performance. Further, the condition is transformed to LMIs.;In practice, the channel uncertainty is an important factor to consider. Therefore in Chapter 4, to incorporate the channel uncertainties, we propose to use the poly-topic uncertainty description, and derive the sufficient condition to guarantee the robust l2 – l ∞, IIR deconvolution filtering performance. In order to further decrease the conservativeness of the design, we apply the parameter-dependent Lyapunov method and improve the robust l2 – l∞ IIR deconvolution filter design.;Finally, several open problems are listed as the future research directions.;In Chapter 2, we consider the design of l2 – l∞ deconvolution filters. We first formulate the FIR deconvolution filtering problem, and then derive the sufficient and necessary condition to satisfy the design objectives. Further, the condition is transformed to LMIs with nonconvex constraints, which can be efficiently solved by the product reduction algorithm (PRA). |
