On the stability of real exponential polynomials with interval-valued delays

We consider the family ? of exponential polynomials. $$f_T (z): = f_0 (z) + f_1 (z)e^{ - zT_1 } + f_2 (z)e^{ - T_2 } + \cdots + f_n (z)e^{ - zT_n } ,T : = T_1 \times T_2 \times \cdots \times T_n ,$$ where thef _k(z),k=0(1)n, are real polynomials under the degree restriction deg(f ₀)>deg(f _k),k=1(1)n, and theT _k,k=1(1)n, are intervals inR ₊. The functions in ? are characteristic functions of linear, retarded dynamical systems with constant coefficients and finitely many interval-valued discrete delays. A stability criterion for ? is expounded; ? is stable if (a) ? contains a stable member and (b) a certain functionalT:S(y) →; {0, 1} vanishes fory in a compact interval inR ₊. Here,S(y) is the boundary of a circular are regionS(y) in the complex plane derived fromf _T. Tools needed for a computer implementation are compiled.     

Differential Maximum Ratio Combining (MRC)-Based Throughput Analysis on Dual-Fading Models of Slotted-Aloha CDMA Systems

In this paper we investigate throughputs of Slotted-ALOHA code division multiple access systems with differential detection upon L-branch antenna by means of maximum ratio combining (MRC) diversity technique. We investigate the effects of co-channel interference by employing two different fading models (i.e. between the desired signals and its interferences.) We consider systems under Nakagami/Nakagami and Rician/Nakagami fading environments. The purpose of employing MRC diversity and differential phase shift keying with L-branch antenna is to overcome multipath fading interference in order to enhance the performance of the systems. Our research indicates that the implementation of L-branch antenna in the receiver have reasonably increased the throughputs of the systems. Furthermore, we also investigate the inverse relation between interference signal and the throughputs of the systems. We further point out that the value of Nakagami fading parameter M and Rician factor K are proportional to the achievable throughputs of the systems.     

Exponential H ∞ Output Tracking Control for Switched Neutral System with Time-Varying Delay and Nonlinear Perturbations

In this paper, the problem of exponential H _∞ output tracking control is addressed for a class of switched neutral system with time-varying delay and nonlinear perturbations. The considered system consists of different neutral and discrete delays. By resorting to the average dwell time approach, a new Lyapunov–Krasovskii functional is proposed to establish sufficient conditions for the exponential stability and H _∞ performance of switched neutral systems. Then, the problem of exponential H _∞ output tracking control is investigated, an explicit expression for the desired exponential tracking controller is also given. Finally, a numerical example is provided to demonstrate the potential effectiveness of the proposed method.     

Positive L_1 Observer Design for Positive Switched Systems

This paper investigates the problem of \(L_1\) observer design for positive switched systems. Firstly, a new kind of positive \(L_1\) observer is proposed for positive switched linear delay-free systems with observable and unobservable subsystems. Based on the average dwell time approach, a sufficient condition is proposed to ensure the existence of the positive \(L_1\) observer. Under the condition obtained, the estimated error converges to zero exponentially, and the \(L_1\) -gain from the disturbance input to the estimated error is less than a prescribed level. Then the proposed design result is extended to positive switched systems with mixed time-varying delays, where the mixed time-varying delays are presented in the form of discrete delay and distributed delay. Finally, two numerical examples are given to demonstrate the feasibility of the obtained results.     

Fundamental spectra of optical functions for indium bromide in the energy range of 2–30 eV at 4.2 K

The spectra of sets of optical fundamental functions are determined for an indium-bromide crystal in the range of 0–30 eV at 4.2 K for the polarizations E ∥ a and E ∥ c. The calculations are carried out using experimental reflection spectra R(E) and several software packages. Their basic features are established.     

MIMO Radar Beamforming Using Orthogonal Decomposition of Correlation Matrix

MIMO radar is the next generation radar which transmits arbitrary waveforms at each one of its apertures. It has been shown that the design of waveforms for MIMO radars in order to synthesize a desired spatial beampattern is mapped into a waveform correlation matrix R design in the narrowband case. As of now, given a desired beampattern or estimated locations information of targets, calculating R has been modeled as an optimization problem like semi-definite programming. Also, in some special cases like rectangular beampattern, closed-form solutions for R has been proposed. In this paper, we introduce a fast algorithm which is capable of designing R in order to achieve more arbitrary beampatterns. Our proposed algorithm is based on eigenvalue decomposition of correlation matrix which employs neither an optimization process nor an iteration one. Furthermore, the proposed algorithm leads to uniform elemental power, low sidelobe level and targets decorrelation which is a great boon, looking from both the hardware and the software perspective. Here, we also introduce a novel algorithm which can work in tandem with the eigenvalue decomposition algorithm and other existing correlation matrix design algorithms to enhance or adapt the designed beampattern.     

Multiple time scales for nonlinear systems

In this paper we extend the results on the multiple time-scale structure for linear autonomous systems of the form $$\dot x = A( \in )x$$ (cf. Coderchet al. [1]) to nonlinear autonomous systems. Our main result is in obtaining conditions under which the linearized system and the nonlinear system around an equilibrium point have the same time-scale structure.     

On Designing Time-Varying Delay Feedback Controllers for Master–Slave Synchronization of Lur'e Systems

This paper is concerned with the problem of designing time-varying delay feedback controllers for master-slave synchronization of Lur'e systems. Two cases of time-varying delays are fully considered; one is the time-varying delay being continuous uniformly bounded while the other is the time-varying delay being differentiable uniformly bounded with the derivative of the delay bounded by a constant. Based on Lyapunov-Krasovskii functional approach, some delay-dependent synchronization criteria are first obtained and formulated in the form of linear matrix inequalities (LMIs). The relationship between synchronization criteria for the two cases of time-varying delays is built. Then, sufficient conditions on the existence of a time-varying delay feedback controller are derived by employing these newly-obtained synchronization criteria. The controller gains can be achieved by solving a set of LMIs. Finally, Chua's circuit is used to illustrate the effectiveness of the design method.     

Donor–Acceptor–Donor Modular Small Organic Molecules Based on the Naphthalene Diimide Acceptor Unit for Solution-Processable Photovoltaic Devices

Two novel solution-processable small organic molecules, 4,9-bis(4-(diphenylamino)phenyl)-2,7-dioctylbenzo[3,8]phenanthroline-1,3,6,8(2H,7H)-tetraone (S6) and 4,9-bis(benzo[b]thiophen-2-yl)-2,7-dioctylbenzo[3,8]phenanthroline-1,3,6,8 (2H,7H)-tetraone (S7), have been successfully designed, synthesized, characterized, and applied in solution-processable photovoltaic devices. S6 and S7 contain a common electron-accepting moiety, naphthalene diimide (NDI), with different electron-donating moieties, triphenylamine (S6) and benzothiophene (S7), and are based on a donor–acceptor–donor structure. S7 was isolated as black, rod-shaped crystals. Its triclinic structure was determined by single crystal x-ray diffraction (XRD): space group \(P\bar{1}\) , Z = 2, a = 9.434(5) Å, b = 14.460(7) Å, c = 15.359(8) Å, α = 67.256(9) degrees, β = 80.356(11) degrees, γ = 76.618(10) degrees, at 150 Kelvin (K), R = 0.073. Ultraviolet–visible absorption spectra revealed that use of triphenylamine donor functionality with the NDI acceptor unit resulted in an enhanced intramolecular charge transfer (ICT) transition and reduction of the optical band gap compared with the benzothiophene analogue. Solution-processable inverted bulk heterojunction devices with the structure indium tin oxide/zinc oxide (30 nm)/active layer/molybdenum trioxide (10 nm)/silver (100 nm) were fabricated with S6 and S7 as donors and (6,6)-phenyl C₇₀-butyric acid methyl ester (PC₇₀BM) as acceptor. Power conversion efficiencies of 0.22% for S6/PC₇₀BM and 0.10% for S7/PC₇₀BM were achieved for the preliminary photovoltaic devices under simulated AM 1.5 illumination (100 mW cm^?2). This paper reports donor–acceptor–donor modular small organic molecules, with NDI as central accepting unit, that have been screened for use in solution-processable inverted photovoltaic devices.     

On centralized and distributed algorithms for minimizing data aggregation time in duty-cycled wireless sensor networks

We study the problem of minimizing data aggregation time in wireless sensor networks (WSNs) under the practical duty-cycle scenario where nodes switch between active states and dormant states periodically for energy efficiency. Under the protocol interference model, we show that the problem is NP-hard and present a lower bound of delay for any data aggregation scheme. To solve the problem efficiently, we then construct a routing tree based on connected dominator set and propose two aggregation scheduling algorithms, which are the centralized Greedy Aggregation Scheduling (GAS) and the distributed Partitioned Aggregation Scheduling (PAS), so as to generate collision-free transmission schedules for data aggregation in duty-cycled WSNs. To minimize the total delay, GAS tries to achieve maximal concurrent transmissions in each time-slot during each frame by using global information, while PAS leverages a network partition based strategy and local information to ensure the largest degree of channel reuse across space and time domains. Theoretical analysis indicates that each algorithm consumes at most \(O(R+\varDelta)\) frames and achieves nearly constant factor approximation on the optimal delay. Here R and \(\varDelta\) are the network radius and the maximum node degree, respectively. We also evaluate the practicability of our algorithms by extensive simulations under various network conditions and the results corroborate our theoretical analysis.     

On the robust control of nonlinear systems

In this paper we consider robust stabilization of the class of nonlinear plants of the form $$\dot x = f(x) + \sum\limits_{i = 1}^m {g_i } (x)u_i (t),$$ which are equivalent, under smooth state space coordinate transformations and nonlinear state feedback, to controllable systems. This approach is very sensitive for unknown parameters' values. Parameter adaptation may be used as a technique to robustify minimum-phase systems [3]. We give an example of a locally stable adaptive tracking system in which the last assumption is weakened. The minimum-phase plant considered in the paper is a current-controlled squirrel cage induction motor.     

HOSVD based multidimensional parameter estimation for massive MIMO system from incomplete channel measurements

The dominant multipath components for massive multiple-input multiple-output systems can be described using geometry-based channel models with R-dimensional (R-D) parameters. These parameters are crucial for channel correlation acquisition, which is a prerequisite for many technical challenges. In this paper, we consider higher-order singular value decomposition based R-D channel modeling parameter estimation from incomplete measurements. Incomplete higher-order orthogonality iteration algorithm can be utilized to solve the problem, which simultaneously achieves tensor recovery and tensor decomposition. After obtaining the signal or noise subspace, the parameters of interest can be estimated by using subspace methods.     

Exponential H∞ filtering for time-varying delay systems: Markovian approach

This paper discusses the H_∞ filtering problem for a class of deterministic systems with time-varying delays, where the stochastic property of time-varying delays described by Markovian approach is taken into consideration in filter design. Firstly, the delay interval is separated into several subintervals, which can be described by Markov process. Then, a new H_∞ filtering method for deterministic system with time-varying delay is given, whose filter can switch with time delay in terms of Markov process. Sufficient conditions for the existence of H_∞ filter are obtained as linear matrix inequalities, where the mode transition rates are known exactly or inexactly. Finally, numerical examples are used to demonstrate the utility of the given methods.     

Some properties of solutions of the semi-state model for nonlinear nonstationary systems

Certain properties of solutions similar to set invariance, set attractivity, boundedness, BIBO stability, etc. are investigated for the semistate model $$P(t)\dot x = M(t,x)x + D(t,x)u,y = q(t,x,u).$$ For systems considered, it is assumed that the reduction to a normal form of lower order is not possible. Using the direct method of Liapunov, the properties of solutions are investigated without actual knowledge of solutions.     

Robust H ∞ Output Tracking Control for a Class of Nonlinear Systems with Time-Varying Delays

This paper addresses the H _∞ output tracking problem for a class of nonlinear systems subjected to model uncertainties and with interval time-varying delay. The stability of the nonlinear time-delay system is analyzed with a novel delay-interval-dependent Lyapunov–Krasovskii functional. Compared to state-of-the-art criteria for linear and nonlinear time-delay systems, less conservative stability conditions are derived with the introduction of new delay-interval-dependent terms and the exploitation of the delay subintervals size. The proposed analysis considers that the delay derivative is either upper and lower bounded, bounded above only, or unbounded, i.e., no restrictions are cast upon the derivative. Numerical examples are provided to enlighten the importance and advantages of the present criterion which outperforms previous criteria in time-delay systems literature. Also, an additional example is provided to highlight the effectiveness of the proposed H _∞ output tracking control design technique for complex nonlinear systems with time-varying delay.     

Minimum delay routing for wireless networks with STDMA

STDMA emerges as a promising channel access technique for providing Quality of Service (QoS) guarantees in multi-hop ad hoc networks such as community mesh and sensor networks. The contention-free channel access combined with spatial reuse of the channel provide significant benefits in the energy/throughput trade-off. On the other hand, the time-multiplexed communication introduces extra delay on the packets when relayed by intermediate nodes. Hence in large wireless sensor networks or mesh networks, where data is routed over several hops before reaching the data sink, STDMA protocols may introduce high end-to-end latency due to the reservation-based access policy. We argue that a suitable routing protocol specifically designed for reservation-based Medium Access Control (MAC) protocols can alleviate their high-latency drawback. Following this argument, we propose first such routing algorithms working on top of a generic STDMA MAC protocol. First, we consider routing with data fusion and present our GreenWave routing idea. We show that our algorithm significantly reduces the end-to-end delay when compared to routing over the shortest-hop paths. Second, we consider routing without data fusion, by taking into account the effect of congestion along the paths on the end-to-end delays. We provide a QIP formulation of the problem, and present a lower bound and a heuristic algorithm to bound the optimal solution. Based on the centralized heuristic algorithm, we propose a distributed, dynamic routing protocol GreenWave routing with Congestion and Flow control (GWCF), which uses a novel congestion and flow control technique utilizing the underlying contention-free protocol. We show by simulations that GWCF routing significantly improves the end-to-end delay while increasing the network throughput when compared to routing over shortest paths.

Structure theorems for nonlinear systems

One of the main results is a proposition to the effect that under some typically mild conditions finite sums of the form $$\sum\limits_\ell {K_\ell \sigma } \left[ {\sum\limits_m {\eta _{\ell m} Q_m (\cdot) + \rho _\ell } } \right]$$ are dense in an important sense in the set of shift-invariant approximately-finite-memory mapsG(·) that take a certain type of subsetU ofR intoR, whereR is the set of real-valued functions defined onR ⁿ orZ ⁿ . Here theQ _m (·) are linear, σ is any element of a certain set of nonlinear maps fromR toR, and the κ_?, ρ_?, and η_?m are real constants. Approximate representations comprising only affine elements and lattice nonlinearities are also presented.     

Cross-virtual concatenation for Ethernet-over-SONET/SDH networks

Ethernet-over-SONET/SDH (EoS) is a popular approach for interconnecting geographically distant Ethernet segments using a SONET/SDH transport infrastructure. It typically uses virtual concatenation (VC) for dynamic bandwidth management. The aggregate SONET/SDH bandwidth for a given EoS connection is obtained by “concatenating” a number of equal-capacity virtual channels. Together, these virtual channels form a virtually concatenated group (VCG). In this article, we introduce a new concatenation technique, referred to as cross-virtual concatenation (CVC), which involves the concatenation of virtual channels of heterogeneous capacities. We show that CVC can be implemented through a simple upgrade at the end node, thus utilizing the existing legacy SDH infrastructure. By employing CVC for EoS systems, we show that the SDH bandwidth can be harvested more efficiently than in conventional VC. We consider two problems associated with routing CVC connections: the connection establishment problem and the connection upgrade problem. The goal of the first problem is to compute a set of paths between two EoS end systems such that a total bandwidth demand and a constraint on the differential delay between the paths are satisfied. Among all feasible sets, the one that consumes the least amount of network bandwidth is selected. For this problem, we develop an integer linear program (ILP) and an efficient algorithm based on the sliding-window approach. For the connection upgrade problem, the goal is to augment an existing set of paths so as to increase the aggregate bandwidth, while continue to meet the differential-delay constraint. We model this problem as a flow-maximization problem with a constraint on the delay of the virtual channels with positive flow. We then consider the problem of path selection under imprecise network state information. Simulations are conducted to demonstrate the advantages of employing CVC and to evaluate the performance of the proposed algorithms.