Fundamental Issues in Guidance and Control of Uncertain Systems

An uncertain linear dynamical system (¿) is described by a state equation whose description includes uncertain parameters. These uncertain parameters are time-varying and enter into the matrices which describe the model and the connection of the inputs to the system. Once a feedback controller has been designed for such a system, it is of interest to know whether asymptotic stability of the system can be guaranteed for all admissible parameter variations within some given bounds. When this turns out to be the case, the system (¿) is said to have the guaranteed stability property. The main results of this paper are summarized as follows: Given the system matrices and bounding sets which describe an uncertain single-input system, we provide necessary and sufficient conditions under which it is possible to design a controller which results in guaranteed stability. Moreover, when the sufficient conditions mentioned above are satisfied, we show that it is possible to provide a "recipe" for construction of the desired controller. A numerical example is used to illustrate the concepts presented herein.