Formation stability is now analyzed under a new prism using input-to-state stability. Formation ISS relates leader input to internal state of the formation and characterizes the way this input affects stability performance. Compared to other notions of stability for interconnected systems, formation ISS does not require attenuation of errors as they propagate, but instead quantifies the amplifi...

This paper deals with concepts of output stability. Inspired in part by regulator theory, several variants are considered, which diier from each other in the requirements imposed upon transient behavior. The main results provide a comparison among the various notions, all of which specialize to input to state stability (iss) when the output equals the complete state.

Fuzzy control systems have had various applications in a wide range of science and engineering in recent years. Since an unstable control system is typically useless and potentially dangerous, stability is the most important requirement for any control system (including fuzzy control system). Conceptually, there are two types of stability for control systems: Lyapunov stability (a special case ...

The analysis of input/output stability is one of the fundamental issues in control theory. External inputs might represent disturbances, estimation errors, or tracking signals, and outputs may correspond to the entire state, or to a more general quantity such as a tracking or regulation error, or the distance to a target set of states such as a desired periodic orbit. For linear systems, one ch...

In this lecture we introduce a useful tool to study the robustness against disturbances of nonlinear systems. Our starting point is the observation that, given a globally asymptotically stable equilibrium, a small enough perturbation of the vector field should not change the phase portrait much, and hence should not destroy the stability properties. However, how large can the perturbations be b...

We consider a class of nonlinear control systems for which stabilizing feedbacks and corresponding Lyapunov functions for the closed loop systems are available. In the presence of feedback delays and actuator errors, we explicitly construct input-tostate stability (ISS) Lyapunov-Krasovskii functionals for the resulting feedback delayed dynamics, in terms of the available Lyapunov functions for ...

This paper studies the emergence of multi-stability and hysteresis in those systems that arise, under positive feedback, starting from monotone systems with well-defined steady-state responses. Such feedback configurations appear routinely in several fields of application, and especially in biology. Characterizations of global stability behavior are stated in terms of easily checkable graphical...

A notion of detectability for nonlinear systems is discussed. Within the framework of “input to state stability” (ISS), a dual notion of “output to state stability” (OSS), and a more complete detectability notion, “input-output to state stability” (IOSS) have appeared in the literature. This note addresses a variant of the IOSS property, using an integral norm to measure signals, as opposed to ...

An input-to-state stability theory, which subsumes results of circle criterion type, is developed in the context of continuous-time Lur’e systems. The approach developed is inspired by the complexified Aizerman conjecture.