New results on stability and L∞‐gain analysis for positive linear differential‐algebraic equations with unbounded time‐varying delays

This article addresses the problems of stability and L_∞‐gain analysis for positive linear differential‐algebraic equations with unbounded time‐varying delays for the first time. First, we consider the stability problem of a class of positive linear differential‐algebraic equations with unbounded time‐varying delays. A new method, which is based on the upper bounding of the state vector by a decreasing function, is presented to analyze the stability of the system. Then, by investigating the monotonicity of state trajectory, the L_∞‐gain for differential‐algebraic systems with unbounded time‐varying delay is characterized. It is shown that the L_∞‐gain for differential‐algebraic systems with unbounded time‐varying delay is also independent of the delays and fully determined by the system matrices. Two numerical examples are given to illustrate the obtained results.     

Small gain problem in coupled differential‐difference equations,time‐varying delays,and direct Lyapunov method

This article presents a Lyapunov–Krasovskii formulation of scaled small gain problem for systems described by coupled differential‐difference equations. This problem includes H_∞ problem with block‐diagonal uncertainty as a special case. A discretization may be applied to reduce the conditions into linear matrix inequalities. As an application, the stability problem of systems with time‐varying delays is transformed into the scaled small gain problem through a process of either one‐term approximation or two‐term approximation. The cases of time‐varying delays with and without derivative upper‐bound are compared. Finally, it is shown that similar conditions can also be obtained by a direct Lyapunov–Krasovskii functional method for coupled differential‐functional equations. Numerical examples are presented to illustrate the effectiveness of the method in tackling systems with time‐varying delays. Copyright © 2010 John Wiley & Sons, Ltd.     

Alternative Method of Solution of the Regulator Equation: L2‐Space Approach

An alternative method for the proof of solvability of the differential equation that is a part of the regulator equation which arises from the solution of the output regulation problem. The proof uses the L²‐space based theory of solutions of partial differential equations for the case of the linear output regulation problem. In the nonlinear case, a sequence of linear equations is defined so that their solutions converge to the solution of the nonlinear problem. This is proved using the Banach Contraction Theorem. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

On the pth moment integral input‐to‐state stability and input‐to‐state stability criteria for impulsive stochastic functional differential equations

In this paper, several new Razumikhin‐type theorems for impulsive stochastic functional differential equations are studied by applying stochastic analysis techniques and Razumikhin stability approach. By developing a new comparison principle for stochastic version, some novel criteria of the pth moment integral input‐to‐state stability and input‐to‐state stability are derived for the related systems. The feature of the criteria shows that time‐derivatives of the Razumikhin functions are allowed to be indefinite, even unbounded, which can loosen the constraints of the existing results. Finally, some examples are given to illustrate the usefulness and significance of the theoretical results.     

Razumikhin‐type theorems on general decay stability and robustness for stochastic functional differential equations

This paper establishes Razumikhin‐type theorems on general decay stability for stochastic functional differential equations. This improves existing stochastic Razumikhin‐type theorems and can make us examine the stability with general decay rate in the sense of the pth moment and almost sure. These stabilities may be specialized as the exponential stability and the polynomial stability. When the almost sure stability is examined, the conditions of this paper may defy the linear growth condition for the drift term, which implies that the theorems of this paper can work for some cases to which the existing results cannot be applied. This paper also examines some sufficient criteria under which this stability is robust. To illustrate applications of our results clearly, this paper also gives two examples and examines the exponential stability and the polynomial stability, respectively. Copyright © 2011 John Wiley & Sons, Ltd.     

Further results on exponential stability of functional differential equations

General non-linear functional differential equations are considered. New explicit criteria for the exponential stability are presented. The stability criteria given in this paper include many existing results as particular cases. In particular, they unify, generalise and improve some ones published recently in [Ngoc, P. H. A. (2012). On exponential stability of non-linear differential systems with time-varying delay. Applied Mathematics Letters, 25(9), 1208–1213 and Ngoc, P. H. A. (2013b). Novel criteria for exponential stability of functional differential equations. Proceedings of the American Mathematical Society, 141(9), 3083–3091]. Two examples are given to show the effectiveness and advantage of the obtained results.     

Sextic C 1-spline collocation methods for solving delay differential equations

In this paper, we propose a global collocation method for the numerical solution of the delay differential equations (DDEs). The method presented is based on sextic C ¹-splines s(x) as an approximation to the exact solution y(x) of the DDEs. Convergence results shows that the error bounds ‖ s ^j ?y ^j ‖=O(h ⁶), j=0, 1, in the uniform norm. Moreover, the stability analysis properties of these methods have been studied. Numerical experiments will also be considered.     

Structured H∞‐control of infinite‐dimensional systems

We develop a novel frequency‐based H_∞‐control method for a large class of infinite‐dimensional linear time‐invariant systems in transfer function form. A major benefit of our approach is that reduction or identification techniques are not needed, which avoids typical distortions. Our method allows to exploit both state‐space or transfer function models and input/output frequency response data when only such are available. We aim for the design of practically useful H_∞‐controllers of any convenient structure and size. We use a nonsmooth trust‐region bundle method to compute arbitrarily structured locally optimal H_∞‐controllers for a frequency‐sampled approximation of the underlying infinite‐dimensional H_∞‐problem in such a way that (i) exponential stability in closed loop is guaranteed and that (ii) the optimal H_∞‐value of the approximation differs from the true infinite‐dimensional value only by a prior user‐specified tolerance. We demonstrate the versatility and practicality of our method on a variety of infinite‐dimensional H_∞‐synthesis problems, including distributed and boundary control of partial differential equations, control of dead‐time and delay systems, and using a rich testing set.     

Existence of Optimal Mild Solutions and Controllability of Fractional Impulsive Stochastic Partial Integro‐Differential Equations with Infinite Delay

In this paper, we investigate a new class of fractional impulsive stochastic partial integro‐differential equations with infinite delay in Hilbert spaces. By using the stochastic analysis theory, fractional calculus, analytic α‐resolvent operator and the fixed point technique combined with fractional powers of closed operators, we firstly give the existence of of mild solutions and optimal mild solutions for the these equations. Next, the controllability of the controlled fractional impulsive stochastic partial integro‐differential systems with not instantaneous impulses is presented. Finally, examples are also given to illustrate our results.     

Interface and bulk effects for bias—light‐illumination instability in amorphous‐In—Ga—Zn—O thin‐film transistors

Abstract— Positive‐current‐bias (PB) instability and negative‐bias—light‐illumination (NBL) instability in amorphous‐In—Ga—Zn—O (a‐IGZO) thin‐film transistors (TFTs) have been examined. The channel‐ thickness dependence indicated that the Vth instability caused by the PB stress is primarily attributed to defects in the bulk a‐IGZO region for unannealed TFTs and to those in the channel—gate‐insulator interface for wet‐annealed TFTs. The interface and bulk defect densities (Dit and Nss, respectively) are Dit = 4.8 × 10¹¹ cm^?2/eV and Nss = 7.0×10¹⁶ cm^?3/eV for the unannealed TFT, which increased to 5.2×10¹¹ cm^?2/eV and 9.8×10¹⁶ cm^?3/eV, respectively, by the PB stress test. These are reduced significantly to Dit = 0.82×10¹¹ cm^?2/eV and Nss = 3.2×10¹⁶ cm^?3/eV for the wet‐annealed TFTs and are unchanged by the PB stress test. It was also found that the photo‐response of a‐IGZO TFTs begins at 2.3 eV of photon excitation, which corresponds to subgap states observed by photoemission spectroscopy. The origin of the NBL instability for the wet‐annealed TFTs is attributed to interface effects and considered to be a trap of holes at the channel‐gate—insulator interface where migration of the holes is enhanced by the electric field formed by the negative gate bias.     

Output‐based H2 optimal controllers for a class of discrete‐time stochastic linear systems with periodic coefficients

The aim of the paper is to present a design procedure of the optimal controller minimizing the H₂‐type norm of discrete‐time stochastic linear systems with periodic coefficients simultaneously affected by a nonhomogeneous but periodic Markov chain and state and control multiplicative white noise perturbations. Firstly, two H₂‐type norms for the linear stochastic systems under consideration were introduced. These H₂‐type norms may be viewed as measures of the effect of the additive white noise perturbations on the regulated output of the considered system. Before deriving of the state space representation of the optimal controller, some useful formulae of the two H₂‐type norms were obtained. These formulae are expressed in terms of periodic solutions of some suitable linear equations and are derived in the absence of some additional assumptions regarding the Markov chain other than the periodicity of the sequence of the transition probability matrices. Further, it is shown that the optimal H₂ controller depends on the stabilizing solutions of some specific systems of coupled Riccati equations, which generalize the well‐known control and filtering equations from linear time invariant case. For the readers convenience, the paper presents iterative numerical algorithms for the computations of the stabilizing solutions of these Riccati type systems. The theoretical developments are illustrated by numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Trajectory Controllability of Fractional Integro‐Differential Systems in Hilbert Spaces

In this paper, sufficient conditions for trajectory controllability of nonlinear fractional integro‐differential systems involving Caputo fractional derivative of order α∈(1,2] in finite and as well as in infinite dimensional Hilbert spaces are obtained. Our tools of study include set‐valued functions, theory of monotone operators and α‐order cosine family of operators. The main results are well illustrated with the aid of examples.     

Large‐signal distributed millimeter‐wave multifinger pHEMT modeling using time‐domain technique

The finite‐difference time‐domain (FDTD) method is used for the large‐signal modeling of a multifinger pHEMT, which is considered as five nonlinear coupled distributed transmission lines. The developed model, which is based on the exact physical layout of multifinger pHEMT, not only accurately describes the propagation effects along the electrodes at higher frequencies but it also includes major nonlinearities of the I–V and Q–V characteristics. Using the transmission line theory, a proper nonlinear equivalent lumped circuit model is allocated for the differential length of the quintuple‐line transistor and the nonlinear active multiconductor transmission line (NAMCTL) equations are derived. These nonlinear, coupled differential equations are numerically solved using the FDTD method. The proposed model is applied to a 100 nm GaAs pHEMT and the simulation results are compared with the results of conventional sliced model in Keysight ADS simulator. The developed transient nonlinear model accurately predicts both the S‐parameters (1–150 GHz) and large‐signal power performances especially at millimeter wave frequency range. The proposed model can be useful in design and analysis of various types of high‐frequency nonlinear integrated circuits.     

H∞ Control for Continuous‐Time Mean‐Field Stochastic Systems

An H_∞‐type control is considered for mean‐field stochastic differential equations (SDEs) in this paper. A stochastic bounded real lemma (SBRL) is proved for mean‐field stochastic continuous‐time systems with state‐ and disturbance‐dependent noise. Based on SBRL, a sufficient condition is given for the existence of a stabilizing H_∞ controller in terms of coupled nonlinear matrix inequalities.     

Dual‐band balanced coupler with wideband common‐mode suppression

A novel compact dual‐band balanced coupler with differential‐mode power division, broadband common‐mode, and common‐to‐differential‐mode conversion suppression is proposed. In these double‐functionality balanced‐coupler architectures, double‐sided parallel‐strip line 180° phase inverters are used to realize the broadband common‐mode rejection. Moreover, the frequency is tunable by changing the characteristic impedance of the transmission line. For practical verification, a balanced couplers (ε_r = 2.65, h = 0.5 mm, tan(δ_D) = 0.003) operation at 0.9/1.8 GHz is constructed in microstrip technology and tested.     

Discretized LKF method for stability of coupled differential‐difference equations with multiple discrete and distributed delays

Time‐delay systems described by coupled differential‐functional equations include as special cases many types of time‐delay systems and coupled differential‐difference systems with time delays. This article discusses the discretized Lyapunov–Krasovskii functional (LKF) method for the stability problem of coupled differential‐difference equations with multiple discrete and distributed delays. Through independently dividing every delay region that the plane regions consists in two delays to discretize LKF, the exponential stability conditions for coupled systems with multiple discrete and distributed delays are established based on a linear matrix inequality (LMI). The numerical examples show that the analysis limit of delay bound in which the systems are stable may be approached by our result. Copyright © 2011 John Wiley & Sons, Ltd.     

A 1‐to‐n way single‐ended‐to‐balanced substrate integrated waveguide filtering power splitter

An approach to 1‐to‐n (n = 3, 4…) way single‐ended‐to‐balanced filtering power splitter (SETBFPS) is proposed. The properly placed balanced ports with 0.5λ_g (λ_g is the substrate integrated waveguide [SIW] guided wavelength at f₀) space make the TE32nd 103 and TE32nd 105 modes of n 32nd‐mode SIW multimode resonators form differential‐mode (DM) passband of the SETBFPS. Compared with the state‐of‐art single‐ended‐to‐balanced power splitters, the proposed approach has all the functions of 1‐to‐n way, filtering, and common‐mode (CM) suppression. A 1‐to‐3 way prototype is exemplified at 3.5 GHz with the minimum insertion loss (IL) of 0.09 dB, a fractional bandwidth (FBW) for a 15‐dB return loss of 35%, and a FBW for 15‐dB CM suppression of 52%. Low IL and wide bandwidth can be observed.     

Characterization of Stochastic Mean‐Field Type Index

index of mean‐field stochastic differential equations (SDE) is investigated in this paper. For systems with state‐ and input‐dependent noise, we obtain a sufficient condition of index larger than some λ>0 via the solvability of differential Riccati equations (DRE). Especially, a necessary and sufficient condition is given for mean‐field SDE with state‐dependent noise, which generalize the corresponding results of classical stochastic systems to the mean‐field stochastic models.     

Wideband and spurious‐suppressed differential bandpass filter based on strip‐loaded slot‐line structure

In this article, a wideband and spurious‐suppressed differential bandpass filter based on strip‐loaded slot‐line structure is presented. By means of the differential microstrip‐slot‐line‐microstrip transition, the proposed filter has a wideband bandpass filtering response. Simultaneously, the utilization of the strip‐loaded slot‐line extends its upper stop‐band. The proposed bandpass filter has wider upper‐stopband, wideband bandpass response, and intrinsic high common‐mode (CM) suppression. To verify the design concept, one filter example has been designed, fabricated, and measured. It has a differential‐mode (DM) 3‐dB fractional bandwidth of 157% with a low 0.82 dB minimum insertion loss. What's more, it shows a very wide 20 dB DM stop‐band bandwidth of 6.5 f_0d. The experienced results are in good agreement with the theoretical and simulated results.