Relaxed ISS Small-Gain Theorems for Discrete-Time Systems

In this paper ISS small-gain theorems for discrete-time systems are stated, which do not require input-to-state stability (ISS) of each subsystem. This approach weakens conservatism in ISS small-gain theory, and for the class of exponentially ISS systems we are able to prove that the proposed relaxed small-gain theorems are non-conservative in a sense to be made precise. The proofs of the small-gain theorems rely on the construction of a dissipative finite-step ISS Lyapunov function which is introduced in this work. Furthermore, dissipative finite-step ISS Lyapunov functions, as relaxations of ISS Lyapunov functions, are shown to be sufficient and necessary to conclude ISS of the overall system.Comment: input-to-state stability, Lyapunov methods, small-gain conditions, discrete-time non-linear systems, large-scale interconnection

Energy transfer within phycocyanin trimers of Mastigocladus laminosus studied by picosecond time-resolved transient absorption spectroscopy

The transient absorption recovery induced in phycocyanin trimers by picosecond pulses of variable wavelength (570 — 620 nm) has been recorded and analyzed by applying a least-squares multi-exponential fit procedure. The results suggest that in native PC trimers the chromophores exhibit a microheterogeneity with the effect that the derived apparent lifetimes are functions of excitation and probing wavelength. It is suggested that, due to strong excitonic coupling between a-84 and ß-84 chromophores, the lifetime of the terminal acceptor state is reduced to about 900 ps; the apparent energy transfer time from chromophore β-155 to a-84 and ß-84 chromophores varies between 20—50 ps depending on the actual chromophore-protein arrangement (microheterogeneity)

Picosecond time-resolved fluorescence of phycobiliproteins

The α- and β-subunits of C-phycocyanin from Mastigocladus laminosus were prepared according to revised procedures. Both subunits are isolated as dimers, which can be dissociated into monomers with detergent mixtures. The fluorescence decay kinetics are similar for the respective monomers and dimers. In no case could they be fitted by only one (α-subunit) or two exponentials (β-subunit) which are predicted by theory for samples with a unique chromophore—protein arrangement containing one and two chromophores, respectively. It is suggested that there exists a heterogeneity among the chromophores of the subunits, which may persist in the highly aggregated complexes present in cyanobacterial antennas

Numerical Construction of LISS Lyapunov Functions under a Small Gain Condition

In the stability analysis of large-scale interconnected systems it is frequently desirable to be able to determine a decay point of the gain operator, i.e., a point whose image under the monotone operator is strictly smaller than the point itself. The set of such decay points plays a crucial role in checking, in a semi-global fashion, the local input-to-state stability of an interconnected system and in the numerical construction of a LISS Lyapunov function. We provide a homotopy algorithm that computes a decay point of a monotone op- erator. For this purpose we use a fixed point algorithm and provide a function whose fixed points correspond to decay points of the monotone operator. The advantage to an earlier algorithm is demonstrated. Furthermore an example is given which shows how to analyze a given perturbed interconnected system.Comment: 30 pages, 7 figures, 4 table

Initial Multidisciplinary Design and Analysis Framework

Within the Supersonics (SUP) Project of the Fundamental Aeronautics Program (FAP), an initial multidisciplinary design & analysis framework has been developed. A set of low- and intermediate-fidelity discipline design and analysis codes were integrated within a multidisciplinary design and analysis framework and demonstrated on two challenging test cases. The first test case demonstrates an initial capability to design for low boom and performance. The second test case demonstrates rapid assessment of a well-characterized design. The current system has been shown to greatly increase the design and analysis speed and capability, and many future areas for development were identified. This work has established a state-of-the-art capability for immediate use by supersonic concept designers and systems analysts at NASA, while also providing a strong base to build upon for future releases as more multifidelity capabilities are developed and integrated

Review on computational methods for Lyapunov functions

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them. Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ di_erent methods such as series expansion, linear programming, linear matrix inequalities, collocation methods, algebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function