Stability Analysis for Variable Sampling Networked Control Systems with Data Packet Dropout and Partly Unknown Transition Probabilities

The stochastic stability and controller design problem for variable sampling network control systems(NCSs) with data packet dropouts and partly unknown transition probabilities are addressed. For the short-delay network control system, the time-varying sampling period is divided into the sum of the constant sampling period and the network induced-delay. The discrete state-space model is formed in which the uncertain part of the sampling period is transformed into uncertainty of the structure parameter. Considering the random data packet dropouts occurring in the sensor-to-controller and controller-to-actuator, the closed-loop NCS is modeled as a discrete-time Markov jump linear system with three modes and partly unknown transition probabilities. Bernoulli random sequence is used to describe the packet dropout and the probability of data dropout is known; Sufficient conditions for the existence of a controller which guarantees the stochastic stability of NCS are established based on stochastic Lyapunov functions, and the linear matrix inequality is solved to obtain the state feedback controller. Finally, a simulations example illustrates the validity and feasibility of the results.