In this paper, we shall provide a new redundant descriptor approach to <i>H</i><sub>∞</sub> state-feedback controller synthesis based on the strategy of the recently developed dilated LMIs. It is known that both of the redundant descriptor and the dilated LMI approaches are effective for robust/gain-scheduled <i>H</i><sub>∞</sub> state-feedback controller synthesis when the state-space matrices of the plant are affected by uncertain/scheduling parameters. These approaches are closely related in the sense that they enlarge the size of LMIs and employ additional matrix variables to obtain more tractable LMI conditions. However, in the existing redundant descriptor approaches, some assumptions have been imposed on the the state-space matrices of the plant to avoid difficulties arising from the fictious direct feedthrough term from the disturbance inputs to the performance outputs of the resulting descriptor form. This is in sharp contrast with the dilated LMI approaches that do not require any specific assumptions on the state space matrices. To fill the gap between these two approaches, in the present paper, we revisit the redundant descriptor approaches and provide a new way to recast the state-space representations into descriptor forms by employing yet new additional variables. By employing those new additional variables, it turns out that those LMIs resulting from the descriptor approaches coincide with the known dilated LMI conditions. The role of those additional variables can be seen clearly if we view from the standpoint of the redundant descriptor approaches.
|Translated title of the contribution||A Redundant Descriptor Approach to <i>H</i><sub>∞</sub> State-Feedback Controller Synthesis:Extension of the Existing Method Based on the Strategy of the Dilated LMIs|
|Number of pages||8|
|Publication status||Published - 2006|