The decentralized robust stabilization and regulation problem subject to gain and phase perturbation

In this paper, the problem of synthesizing a decentralized controller for a descriptor plant subject to uncertainty in gain and phase is considered. Decentralized stabilization and regulation of descriptor type systems is generally more difficult than regular state-space processes due to the existence of impulsive modes and decentralized fixed modes. Related to the decentralized stabilization and regulation problems is the issue of robustness. Properties of decentralized descriptor systems subject to structured multivariable gain and phase perturbation are reported in this paper. In particular, results are given to determine if a descriptor system possesses a non-zero impulsive gain margin. Furthermore, it is shown that if a plant is open-loop unstable with at least two control agents, then for almost all plants, any controller which stabilizes the system has no gain margin. Finally, it is shown that if a plant is open-loop stable with no impulsive modes, then there exists a solution to the generalized decentralized robust servomechanism problem with any gain margin, time lag margin specification, iff there exists a solution to the generalized decentralized robust servomechanism problem for the plant