Analysis and design of networked control systems with long delays based on Markovian jump model

A mathematical model of networked control systems (NCS) with dynamic controllers is presented when the network-induced random time-varying delays of NCS are bounded and the upper bound of which is longer than one sampling period. This paper discretizes the model of continuous-time systems, applies augmented state-space method to the model and builds a discrete-time jump system model governed by a finite state Markov process. And the necessary and sufficient conditions guaranteeing stability of the system are discussed. This paper applies interior-point algorithm to design stabilizing controllers, presents a method to get the feasible initial solution and replaces Newton direction which is generally used in the interior-point algorithm with conjugate gradient direction for simplifying the algorithm. And this improved algorithm stated above is applied effectively to the networked control system of a cart and inverted pendulum with long delays.