TPτ Model Transformation: A Systematic Modelling Framework to Handle Internal Time Delays in Control Systems

Varying time delays are inherent and unavoidable properties of a large set of control systems causing stability issues in most cases. Control design methods that guarantee the stability, such as those based on the Lyapunov–Krasovskii functional, are mathematically highly complicated and therefore have hardly spread into everyday engineering practice. This paper introduces a systematic modelling and control design schema enabling a gateway between the different delayed system representations and the tensor product (TP) type convex polytopic models which allows the direct use of linear matrix inequality (LMI)‐based controller and observer synthesis. The approach presented assumes known, bounded, time‐varying internal time‐delays where the delay derivative is not considered. The proposed modelling scheme is demonstrated via a numerical example.