Observer-Based l2 − l∞ Control for Singularly Perturbed Semi-Markov Jump Systems with An Improved Weighted TOD Protocol

The $l_{2}-l_{\\infty }$ stabilization issue for discrete-time networked singularly perturbed semi-Markov jump systems under the observer-based scheme is investigated in this paper. For networked systems, the measurement outputs are quantized before transmission. Moreover, an improved protocol generalizing the traditional weighted try-once-discard protocol is established to further optimize the utilization of communication resources. In contrast to the previous stabilization analysis for discrete-time semi-Markov jump systems, a novel processing method is proposed, based on which the $l_{2}-l_{\\infty }$ performance analysis for the investigated systems can be achieved effectively. Furthermore, two new constraints relevant to the improved protocol are constructed to obtain less conservatism results. Via constructing a piecewise Lyapunov function related to both the semi-Markov process and the improved protocol information, sufficient conditions which ensure that the closed-loop system is $\\delta$-error mean-square stable with a prescribed performance property are developed. Ulteriorly, the observer parameters and the controller gains can be co-designed by solving a convex optimization problem. A concise example is finally employed to demonstrate the validity and potential of the proposed scheme.