A New Polytopic Approximation Method for Networked Systems with Time-Varying Delay

Introducing a network into a control loop brings great challenges as well as benefits to the system. Some network-induced imperfections, such as time-varying delays, may constitute obstacles for control tasks. In discrete-time modeling approaches for linear networked control systems with time-varying delays, discrete-time models with uncertainties appearing in an exponential form are usually obtained. To make such models suitable for stability analysis, several different methods have been proposed in the literature to approximate the origin models as polytopic models. This brief proposes a new polytopic approximation method using a simplex type of geometrical construction under the assumption that the eigenvalues of system matrix $A$ are all real and varied. Relatively fewer vertices are needed to construct the polytopic model. Stability conditions for the polytopic model are developed and presented in terms of linear matrix inequalities. Qualitative comparisons between the proposed method and some existing methods in aspects of computing complexity and conservatism are made by applying them to a benchmark example.