Delay-dependent exponential stabilization for uncertain linear systems with interval non-differentiable time-varying delays

In this paper, the problem of exponential stabilization for a class of linear systems with time-varying delay is studied. The time delay is a continuous function belonging to a given interval, which means that the lower and upper bounds for the time-varying delay are available, but the delay function is not necessary to be differentiable. Based on the construction of improved Lyapunov-Krasovskii functionals combined with Leibniz-Newton’s formula, new delay-dependent sufficient conditions for the exponential stabilization of the systems are first established in terms of LMIs. Numerical examples are given to demonstrate that the derived conditions are much less conservative than those given in the literature.     

Photoreduction of viologen-containing vinyl polymers by 2-propanol

In order to study the role of viologen-containing vinyl polymers in light energy conversion systems, the photoreduction of the polymer by 2-propanol and the properties of the reduced polymer were studied in comparison with methylviologen. There were marked polymer effects in the initial rate of photoreduction as well as in the absorption spectra of the photoreduced species. Both effects were interpreted in terms of the local concentration effect of viologen units in the photoreduction step. The spectral difference was found to be due to the dimeric association of the reduced viologen units on the polymer.     

An improved stability criterion for a class of neutral differential equations

This work gives an improved criterion for asymptotical stability of a class of neutral differential equations. By introducing a new Lyapunov functional, we avoid the use of the stability assumption on the main operators and derive a novel stability criterion given in terms of a LMI, which is less restricted than that given by Park [J.H. Park, Delay-dependent criterion for asymptotic stability of a class of neutral equations, Appl. Math. Lett. 17 (2004) 1203–1206] and Sun et al. [Y.G. Sun, L. Wang, Note on asymptotic stability of a class of neutral differential equations, Appl. Math. Lett. 19 (2006) 949–953].     

FRET detection of Octamer-4 on a protein nanoarray made by size-dependent self-assembly

An alternative approach for fabricating a protein array at nanoscale is suggested with a capability of characterization and/or localization of multiple components on a nanoarray. Fluorescent micro- and nanobeads each conjugated with different antibodies are assembled by size-dependent self-assembly (SDSA) onto nanometer wells that were created on a polymethyl methacrylate (PMMA) substrate by electron beam lithography (EBL). Antibody-conjugated beads of different diameters are added serially and electrostatically attached to corresponding wells through electrostatic attraction between the charged beads (confirmed by zeta potential analysis) and exposed p-doped silicon substrate underneath the PMMA layer. This SDSA method is enhanced by vibrated-wire-guide manipulation of droplets on the PMMA surface containing nanometer wells. Saturation rates of antibody-conjugated beads to the nanometer patterns are up to 97% under one component and 58–70% under two components nanoarrays. High-density arrays (up to 40,000 wells) could be fabricated, which can also be multi-component. Target detection utilizes fluorescence resonance energy transfer (FRET) from fluorescent beads to fluorescent-tagged secondary antibodies to Octamer-4 (Oct4), which eliminates the need for multiple steps of rinsing. The 100 nm green beads are covalently conjugated with anti-Oct4 to capture Oct4 peptides (39 kDa); where the secondary anti-Oct4 and F(ab)₂ fragment of anti-gIgG tagged with phycoerythrin are then added to function as an indicator of Oct4 detection. FRET signals are detected through confocal microscopes, and further confirmed by Fluorolog3 spectrofluorometer. The success rates of detecting Oct4 are 32% and 14% of the beads in right place under one and two component nanoarrays, respectively. Ratiometric FRET is used to quantify the amount of Oct4 peptides per each bead, which is estimated about 2 molecules per bead.     

Parameter-dependent <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> Control for Time-varying Delay Polytopic Systems

This paper addresses the robust stabilization and H _∞ control problem for a class of linear polytopic systems with continuously distributed delays. The control objective is to design a robust H _∞ controller that satisfies some exponential stability constraints on the closed-loop poles. Using improved parameter-dependent Lyapunov Krasovskii functionals, new delay-dependent conditions for the robust H _∞ control are established in terms of linear matrix inequalities.     

Switching design for exponential stability of a class of nonlinear hybrid time-delay systems

This paper addresses the exponential stability for a class of nonlinear hybrid time-delay systems. The system to be considered is autonomous and the state delay is time-varying. Using the Lyapunov functional approach combined with the Newton–Leibniz formula, neither restriction on the derivative of time-delay function nor bound restriction on nonlinear perturbations is required to design a switching rule for the exponential stability of nonlinear switched systems with time-varying delays. The delay-dependent stability conditions are presented in terms of the solution of algebraic Riccati equations, which allows computing simultaneously the two bounds that characterize the stability rate of the solution. A simple procedure for constructing the switching rule is also presented.     

Exponential stabilization for a class of hybrid systems with mixed delays in state and control

This paper proposes a switching design for the exponential stabilization problem of hybrid systems with mixed time-delays in both the state and control. By using an improved Lyapunov–Krasovskii functional, a memoryless switching controller for the exponential stabilization of the system is designed in terms of linear matrix inequalities. The approach also allows us to compute simultaneously the two bounds that characterize the exponential stability rate of the solution.     

LMI approach to exponential stability of linear systems with interval time-varying delays

This paper addresses exponential stability problem for a class of linear systems with time-varying delay. The time delay is assumed to be a continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a set of augmented Lyapunov–Krasovskii functional combined with the Newton–Leibniz formula technique, new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of linear matrix inequalities (LMIs). An application to exponential stability of uncertain linear systems with interval time-varying delay is given. Numerical examples are given to show the effectiveness of the obtained results.     

Full‐Order observer design for nonlinear complex large‐scale systems with unknown time‐varying delayed interactions

This article is concerned with the problem of state observer for complex large‐scale systems with unknown time‐varying delayed interactions. The class of large‐scale interconnected systems under consideration is subjected to interval time‐varying delays and nonlinear perturbations. By introducing a set of argumented Lyapunov–Krasovskii functionals and using a new bounding estimation technique, novel delay‐dependent conditions for existence of state observers with guaranteed exponential stability are derived in terms of linear matrix inequalities (LMIs). In our design approach, the set of full‐order Luenberger‐type state observers are systematically derived via the use of an efficient LMI‐based algorithm. Numerical examples are given to illustrate the effectiveness of the result. © 2014 Wiley Periodicals, Inc. Complexity 21: 123–133, 2015