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.