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In this paper the input-to-state stability (iss) property is studied for discrete-time nonlinear systems. We show that many iss results for continuous-can be extended to the discrete-time case. More precisely, we provide a Lyapunov-like sufficient condition for iss, and we show the equivalence between the iss property and various other properties. Utilizing… (More)
The notion of input to state stability (iss) is now recognized as a central concept in nonlinear systems analysis. It provides a nonlinear generalization of nite gains with respect to supremum norms and also of nite L 2 gains. It plays a central role in recursive design, coprime factoriza-tions, controllers for non-minimum phase systems, and many other… (More)
Continuous queries are persistent queries that allow users to receive new results when they become available. While continuous query systems can transform a passive web into an active environment, they need to be able to support millions of queries due to the scale of the Internet. No existing systems have achieved this level of scalability. NiagaraCQ… (More)
This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical theorems. In a unified and natural manner, it (1) allows arbitrary bounded time-varying parameters in the system description, (2) deals with global asymptotic stability,… (More)
The goal of this paper is to provide a Lyapunov statement and proof of the recent nonlinear small-gain theorem for interconnected input/state-stable (ISS) systems. An ISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for both the subsystems. The notion of nonlinear gains has recently been acknowledged as… (More)
We show that the well-known Lyapunov sufficient condition for "input-to-state stability" (ISS) is also necessary, settling positively an open question raised by several authors during the past few years. Additional characterizations of the ISS property, including one in terms of nonlinear stability margins, are also provided.
XML has become the de facto standard format for web publishing and data transportation. Since online information changes frequently, being able to quickly detect changes in XML documents is important to Internet query systems, search engines, and continuous query systems. Previous work in change detection on XML, or other hierarchically structured… (More)
This paper presents a converse Lyapunov theorem for discrete-time systems with disturbances taking values in compact sets. Among several new stability results, it is shown that a smooth Lyapunov function exists for a family of time-varying discrete systems if these systems are robustly globally asymptotically stable.
This work explores Lyapunov characterizations of the input-output-to-state stability (ioss) property for nonlinear systems. The notion of ioss is a natural generalization of the standard zero-detectability property used in the linear case. The main contribution of this work is to establish a complete equivalence between the input-output-to-state stability… (More)
— We present new characterizations of the Input to State Stability property. As a consequence of these results , we show the equivalence between the ISS property and several (apparent) variations proposed in the literature.