Robust Servomechanism Problem for Descriptor-Type Systems with Distributed Time-Delay

The dynamics of many systems may be described by differential equations coupled with algebraic equations. Such systems are usually termed as descriptor-type systems. Furthermore, the dynamics of many such systems may be subject to time-delays, which may have a distributed nature. Thus, the dynamics of such systems are, in fact, described by distributed delay -differential equations coupled with distributed-delay algebraic equations. This paper considers the robust servomechanism problem, which is to design a controller such that the overall closed-loop system is globally asymptotically stable and its output tracks a given reference signal in the presence of certain disturbances and modeling uncertainties, for systems described by distributed-delay-differential equations coupled with distributed-delay-algebraic equations. The necessary and sufficient conditions for the solvability of this problem are given and, when a solution exists, the structure of the controller which solves this problem is presented.