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This paper presents a new delay system approach to network-based control. This approach is based on a new time-delay model proposed recently, which contains multiple successive delay components in the state. Firstly, new results on stability and H ∞ performance are proposed for systems with two successive delay components, by exploiting a new Lyapunov-Krasovskii functional and by making use of novel techniques for time-delay systems. An illustrative example is provided to show the advantage of these results. The second part of this paper utilizes the new model to investigate the problem of network-based control, which has emerged as a topic of significant interest in the control community. A sampled-data networked control system with simultaneous consideration of network induced delays, data packet dropouts and measurement quantization is modeled as a nonlinear time-delay system with two successive delay components in the state and, the problem of network-based H ∞ control is solved accordingly. Illustrative examples are provided to show the advantage and applicability of the developed results for network-based controller design. ᭧

Abstract-This note is concerned with the stability analysis of discrete-time systems with time-varying state delay. By defining new Lyapunov functions and by making use of novel techniques to achieve delay dependence, several new conditions are obtained for the asymptotic stability of these systems. The merit of the proposed conditions lies in their less conservativeness, which is achieved by circumventing the utilization of some bounding inequalities for cross products between two vectors and by paying careful attention to the subtle difference between the terms ( ) and ( ), which is largely ignored in the existing literature. These conditions are shown, via several examples, to be much less conservative than some existing result.

This paper investigates the problem of robust estimation for uncertain systems subject to limited communication capacity. The parameter uncertainty belongs to a given convex polytope and the communication limitations include measurement quantization, signal transmission delay, and data packet dropout, which appear typically in a network environment. The problem of filter design is first solved for a nominal system subject to the aforementioned information limitations, which is then extended to the uncertain case based on the notion of quadratic stability. To further reduce the overdesign in the quadratic framework, this paper also proposes a parameter-dependent filter design procedure, which is much less conservative than the quadratic approach. The quadratic and parameter-dependent approaches provide alternatives for designing robust filters with different degrees of conservativeness and computational complexity. Two examples, including a mass-spring system, are utilized to illustrate the design procedures proposed in this paper.Index Terms-Data packet dropout, measurement quantization, networked control systems (NCSs), robust estimation, signal transmission delay.

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