Sanfelice and rafael fierro abstractthis paper investigates stability of nonlinear con trol systems under intermittent information. Smallgain theorem for iss systems and applications. Abstracta new version of the smallgain theorem is presented for nonlinear finite dimensional systems. Pdf a local small gain theorem for discretetime systems. A nonlinear smallgain theorem for largescale time delay systems. On the application of the smallgain theorem to the stability analysis. A tight smallgain theorem for not necessarily iss systems. Indeed, this feature is illustrated by many examples in the paper. Optimal output modification and robust control using minimum. The result provides conditions for global asymptotic. This new smallgain theorem applies to behaviors beyond bounded deviation from a nominal point to include a fragment of linear temporal.
In particular, a small gain theorem for l 2 stable systems has been developed in the early work of hillmoylan. Finally, we introduce variations of asymptotic gain and limit. Here is a formal presentation of a one version of the small gain theorem the rest are formulated and proven in a similar way. Mimo nyquist interpretation of the large gain theorem. A small gain theorem for parametric assumeguarantee contracts.
Pdf a nonlinear smallgain theorem for largescale time. Another feature, which is not frequently recognised, is that vector lyapunov functions can handle largescale systems more easily than single lyapunov functions. While the smallgain theorem to be introduced in this paper retains the abovementioned features of our earlier nonlinear iss smallgain theorem, it will enjoy an additional new feature, that is, both finitedimensional and infinitedimensional systems can be addressed. We take violation of the smallgain condition to be the. Chapter 3 small gain theorem and integral quadratic. Pdf the notion of local lpstability is defined, and a local version of the small gain theorem is established. Building on the smallgain theorem, we develop selftriggered control yielding stable closedloop systems. Smallgain theorem for iss systems and applications centre. G has its input w and output v partitioned according to wt w 0t w 1t. G has its input w and output v partitioned according to wt w 0t w 1t, vt v 0t v 1t.
A lyapunovbased smallgain theorem for infinite networks. The work on small gain theorems for the nonlinear case began with the work 12, where a nonlinear generalization of the classical small gain theorem was proposed for both continuous and discretetime feedback systems. Proceedings of the ieee conference on decision and control 191. Pdf a small gain theorem for systems with noncausal. Building on the small gain theorem, we develop selftriggered control yielding stable closedloop systems. The large gain theorem is an inputoutput stability result with intriguing applications in the field of control systems. A small gain theorem for systems with noncausal subsystems. This paper presents a smallgain theorem for networks composed of a countably infinite number of finitedimensional subsystems. Download free acrobat reader dc software, the only pdf viewer that lets you read, search, print, and interact with virtually any type of pdf file. Sanfelice and rafael fierro abstractthis paper investigates stability of nonlinear control systems under intermittent information. We derive in this work a local nonlinear smallgain theorem in the framework of inputtostate stability for discrete time systems. While this theorem admits a very simple formulation in the case of linear systems see e.
On the application of the smallgain theorem to the stability analysis of largescale power systems with delay. A vector smallgain theorem for general nonlinear control. Here we mainly focus on timedelay systems described by. Small gain theorems for general networks of heterogeneous infinite. A vector small gain theorem 311 functions for the case of iss stability. In nonlinear systems, the formalism of inputoutput stability is an important tool in studying the stability of interconnected systems since the gain of a system. The basic formulation of the small gain theorem concerns an interconnection of two systems as shown on figure.