An Output Feedback Multivariable PD-Controller Design Method for Time Delay Systems: A New LMI Approach

This paper investigates the problem of designing a static output feedback controller and a PD multivariable static output feedback controller for linear time delay systems within the LMI framework. The main advantage of the proposed approach is its powerful ability to decouple the input and the output gain matrices leading to synthesize the controller gain matrix through linear matrix inequalities (LMI) technique. The synthesis conditions are thus formulated in LMI form which avoids the use of any iterative approach to resolve the feasibility problem. Moreover, the use of a PD multivariable type of static output feedback controller provides more information to the time delay control systems which results in achieving more improvement on the maximum admissible delay bound. From this point of view, it brings light on the expectation that if the controller is built up by as much information as possible, there exists a potential room for further improvement. In addition, it appears that the aim and thus the requirement of an LMI sort of formulation needs a reduced form of use of the free weighting matrices. Therefore, the challenge of an LMI formulation with the most generalistic attitude remains still open. Besides, the proposed methodology can be easily extended to time delay systems subject to time varying delay and/or model uncertainties, parameter perturbations and external disturbances. Finally, a dynamic output feedback can also be taken into consideration in a similar manner with the developed technique of the present work. A numerical example is presented to illustrate the application of the developed results. The numerical results indicate that some improvements on the maximum admissible delay bound are achieved with the proposed methodology in comparison to that reported in the literature.