H-infinity Design in Interconnected and Slowly Time-varying Systems

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This project is concerned with the problem of system design in an Hoo sense for interconnected and slowly time-varying systems. The project starts with the modification of the Hoo method so that the effect of interaction among coupled subsystems can be incorporated into the design. In particular, we will develop a design strategy which exploits the available design freedom contained in Hoo method to achieve coordination of subsystems. Furthermore, we will investigate the design tradeoff and limits on achievable performance in Hoo design of interconnected systems. The project continues to study the problem of stabilization and optimization in continuous-time slowly time-varying (possibly unstable) systems containing possibly time-varying delay terms. The frozen-time approach will be employed to derive practical design procedures, and will be examined for its limitations. The local- global double algebra framework developed by the Principal Investigator and Zames will be used to study rigorously the issues of stabilization and optimization in slowly time-varying systems. We will concentrate on the following fundamental issues in Hoo design problems for slowly time-varying systems: (1) the development of analysis tools for robust stability and performance, (2) the construction of feedback controllers, (3) the power of adaptation as compared with general time- varying system design, and (4) the limits of achievable performance imposed by plant dynamics. The project will be of practical importance in providing constructive design tools, and of theoretical significance in giving a better understanding of the limitations of the frozen-time approach and adaptation, and the relationships between modeling and design.