Santa Barbara Delay Impulsive Systems : A Framework For Modeling Networked Control Systems

Delay Impulsive Systems: A Framework For Modeling Networked Control Systems by Payam Naghshtabrizi We model Networked Control Systems (NCSs) with variable delay, sampling intervals and packet dropouts as delay impulsive systems which exhibit continuous evolutions described by ODEs and state jumps or impulses that experience delay. We develop theorems for the exponential stability of nonlinear time-varying delay impulsive systems which can be viewed as extensions of the LyapunovKrasovskii Theorem for time-delay systems. For linear plants and controllers, exponential stability conditions can be formulated as Linear Matrix Inequalities (LMIs), which can be solved numerically. By solving these LMIs, one can find classes of delay-sampling sequences for the different sample-hold pairs in a NCS such that exponential stability is guaranteed. The timing requirements of delay-sampling sequences can be met by deterministic networks for which delivery of packets can be guaranteed with bounded delay. Scheduling theory provides conditions to check whether all the timing requirements can be met. If appropriate scheduling conditions are satisfied, the network will in fact be capable of delivering all the packets on time, and stability of all systems connected to the network is guaranteed. Our analysis leads to the x design of communication protocols to determine which nodes gain access to the network and an algorithm to select sampling sequences. We also consider the tracking problem over the network. A feedforward structure is used to force the state of the plant to follow a desired trajectory and feedback structure is used to obtain the desired performance and robustness. Since the feedback and the feedforward control commands are sampled and experience variable delays, exact trajectory tracking is not possible and there is an error between the desired trajectory and the real trajectory of the system. The error dynamics can be modeled as an impulsive system driven by an external input corresponding to feedforward signal mismatch. Sufficient condition for the Inputto-State Stability (ISS) of the tracking error dynamics with respect to this input is given. These results also provide classes of sampling-delay sequences for which the steady-state tracking error is guaranteed to be smaller than a desired level.