H∞ control for stochastic stability and disturbance attenuation in a class of networked hybrid systems

The authors study H_∞ control for stochastic stability and disturbance attenuation (SSDA) in a class of networked hybrid systems (NHS). A hybrid system has both continuous variables and discrete events. A NHS consists of a set of subsystems that are coupled together. Both continuous dynamics and coupling among subsystems change as events occur. When an event occurs stochastically, the continuous state variables may jump from one value to another. Using the stochastic Lyapunov functional approach, sufficient conditions on the existence of an H_∞ state-feedback controller that ensures stochastic stability and H_∞ disturbance attenuation for NHS with and without time delays are obtained. The derived conditions are expressed in terms of solutions of appropriate algebraic inequalities. A new approach to the design of such a controller is then presented. An illustrative example of a unified chaotic network with randomly jumping parameters is used to demonstrate the satisfactory control performance.