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.
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 nucleus isthmi pars magnocellularis (Imc) and pars parvocellularis (Ipc) influence the receptive field structure of neurons in the optic tectum (TeO). To understand better the anatomical substrate of isthmotectal interactions, neuronal morphology and connections of Imc were examined in chicks (Gallus gallus). Cholera toxin B injection into TeO… (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.
Differential innervation of segregated dendritic domains in the chick nucleus laminaris (NL), composed of third-order auditory neurons, provides a unique model to study synaptic regulation of dendritic structure. Altering the synaptic input to one dendritic domain affects the structure and length of the manipulated dendrites while leaving the other set of… (More)
We propose a definition of detectability for nonlinear systems. This definition generalizes naturally the standard property in the linear case, and is consistent with the " input to state stability " approach to controlled stability. We provide a characterization in terms of a dissipation inequality involving storage (Lyapunov) functions.
Previous characterizations of iss-stability are shown to generalize without change to the case of stability with respect to sets. Some results on iss-stabilizability are mentioned as well.
Germline mutations in the RAS/ERK signaling pathway underlie several related developmental disorders collectively termed neuro-cardio-facial-cutaneous (NCFC) syndromes. NCFC patients manifest varying degrees of cognitive impairment, but the developmental basis of their brain abnormalities remains largely unknown. Neurofibromatosis type 1 (NF1), an NCFC… (More)
This paper continues the study of the integral input-to-state stability (iiss) property. It is shown that the iiss property is equivalent to one which arises from the consideration of mixed norms on states and inputs, as well as to the superposition of a " bounded energy bounded state " requirement and the global asymptotic stability of the unforced system.… (More)
Atmospheric aerosols affect weather and global general circulation by modifying cloud and precipitation processes, but the magnitude of cloud adjustment by aerosols remains poorly quantified and represents the largest uncertainty in estimated forcing of climate change. Here we assess the effects of anthropogenic aerosols on the Pacific storm track, using a… (More)