Control of linear time-varying systems based on finite difference method

Growing attention has been devoted to adaptive control of time-varying systems. There exist many approaches to this problem, such as model reference control, variable structure control, and the use of multiple models, switching, or tuning control. However, these methods seem to be too complicated to be widely used in industries and engineering applications. This paper puts forward a simple method for control of a linear time-varying system. Instead of analyzing and controlling the system in the whole time domain, the process is first discretized and in each time step the plant model is then greatly simplified in a way that the desired dynamic and steady response of the system can be achieved. Hence, time-varying systems, which are difficult to control, and which were controlled by the conventional adaptive control method, can be controlled by the new simple method easily and successfully. The algorithm is illustrated and basic steps explained through an example solved at the end of the paper.