Robust stabilization of Networked Control Systems using the Markovian jump system approach

The key feature of Networked Control Systems (NCSs) is that the information is exchanged through a network among control system components. Transmitting control signals through shared networks induces time delays and data losses which may destabilize the system. This time delay may be constant periodic or random. The random time delay can be modeled using Markov Chains and the NCS can be modeled as Markovian jump system. The stochastic stability of the system has the form of Bilinear Matrix Inequality (BMI). The V-K iteration algorithm is used to solve the BMI and hence to design the stabilizing controller. A modified V-K iteration algorithm is presented in this paper where the decay rate is maximized in both the V- and K-loops. The V-K algorithm method is applied to the cart and inverted pendulum problem which shows that the decay rate is improved with the modified algorithm.