Control of Networked Systems With Asynchronous Sensor and Controller Over a Lossy Network

In this article, the stability analysis and synthesis issues of networked control systems with asynchronous sensors and controllers are studied, where the stochastic variable obeying a certain probability distribution is introduced to characterize the clock offset between the sensor and the controller. First, a continuous-time framework covering random clock offsets and consecutively lost packets is established. An appropriate discrete-time stochastic augmented model is then constructed to investigate the analysis and synthesis problems of resulting continuous-time framework. Therefore, we prove that the stochastic stability of the discrete-time model implies the stochastic stability of resulting continuous-time system. Based on the discrete-time stochastic augmented model, the random and highly nonlinear terms are decoupled with the help of the law of total expectation, Kronecker product operation, and reduced-order confluent Vandermonde matrix. Subsequently, we present the stability condition in the form of linear matrix inequality and design the desired gain matrix such that the original continuous-time system is stochastically stable. Finally, two numerical examples and a practical example are utilized to clarify the practicability of the designed strategy.