Control of second order strictly proper unstable systems with time delay

This paper considers the stabilization and control of linear time invariant systems containing two unstable poles, a "stable" zero and time delay. It is well known that time delays complicate the stability analysis and the design of appropriate control strategies. For this reason, we propose a simple control strategy based on an observer system with the aim of stabilize this class of systems. Necessary and suffcient conditions are stated in order to guarantee the stability of the closed loop system. Once the stability conditions are satisfied, only the plant model and four proportional gains are enough in order to implement the proposed control strategy. Finally, some examples are presented in order to illustrate the proposed control strategy performance, showing some robustness when uncertainties are presented in the time delay value.