ABSTRACT This paper introduces a new framework for the control of networked control systems (NCSs) consisting of a continuous‐time plant, a discrete‐time controller, and a wireless network with delays, via the differential linear matrix inequality (DLMI)‐based approach. We first derive a hybrid linear system (HLS) representation of NCSs by defining two flow dynamic equations before and after the sampling instants and one jump equation at the sampling instants. Based on the HLS representation, we derive a DLMI‐based necessary and sufficient condition for the exponential stability of NCSs with known constant delays. This also allows us to establish a controller ensuring that the NCS is exponentially stable and the resulting ‐gain is less than a pre‐given . The relevant arguments are further extended to a more involved problem of NCSs with time‐varying unknown delays. In other words, we obtain some DLMI‐based conditions characterizing the exponential stability and a controller synthesis for suppressing the ‐gain of such networked systems. Finally, numerical examples are provided to validate the effectiveness of the proposed DLMI‐based arguments.
Park et al. (Thu,) studied this question.