Reducible linear time-varying control systems†

Linear systems with time-varying coefficients are of great concern in various fields. However, the theoretical treatment is very difficult and very few achievements have been seen so far. In this paper, the discussions are confined to those classes of systems which can be transformed into linear stationary systems. These systems are known as the ‘reducible systems’. First, a sufficient condition is shown for a system consisting of reducible sub-systems to be reducible. A few examples are shown in relation to this condition. Further discussed are some applied problems such as the compensation of unstable systems and the optimal control of reducible systems, where the adjoint of a reducible system is shown to be reducible.