The effects of government subsidies on decentralised reverse supply chains

This paper examines the impacts of exogenous government subsidies on recycled material flows in decentralised reverse supply chains where players behave according to their own interests. We present a four-tiered network equilibrium model consisting of the sources of electronic scrap products and the collectors, processors and demand markets. We mathematically transform the players’ optimality conditions governing players’ behaviours into a variational inequality formulation. We investigate the impact of alternate schemes of government subsidies on the equilibrium amount, subsidy effectiveness and subsidy elasticity. The real-world case study shows that subsidising the tier of processors demonstrates the superiority of the investigated performance measures.     

Stabilization of uncertain linear distributed delay systems with dissipativity constraints

This paper examines the problem of stabilizing linear distributed delay systems with nonlinear distributed delay kernels and dissipativity constraints. Specifically, the nonlinear distributed kernel includes functions such as polynomials, trigonometric and exponential functions. By constructing a Liapunov–Krasovskii functional related to the distributed kernels, sufficient conditions for the existence of a state feedback controller which stabilizes the uncertain distributed delay systems with dissipativity constraints are given in terms of linear matrix inequalities (LMIs). In contrast to existing methods, the proposed scenario is less conservative or requiring less number of decision variables based on the application of a new derived integral inequality. Finally, numerical examples are presented to demonstrate the validity and effectiveness of the proposed methodology.     

Decentralized adaptive command following and disturbance rejection for subsystems with local full‐state feedback

We present a decentralized model reference adaptive control method, where each local controller uses full‐state feedback from the local subsystem. The controller is strictly decentralized, meaning that no information (including reference‐model trajectories) is shared between local controllers. This decentralized controller achieves stabilization, command following, and disturbance rejection provided that the reference‐model commands and the disturbances are sinusoidal with known spectrum. The controller is effective for multi‐input subsystems with arbitrarily large subsystem interconnections. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust Control of Permanent Magnet Synchronous Motors

In this paper, permanent magnet synchronous motors (PMSMs) are investigated. According to the feature of PMSMs, a novel state equation of PMSMs is obtained by choosing suitable state variables. Based on the state equation, robust controllers are designed via interval matrix and PI control idea. In terms of bilinear matrix inequations, sufficient conditions for the existence of the robust controller are derived. In order to reduce the conservation and the dependence on parameter, the control inputs of PMSMs are divided into two parts, a feedforward control input and a feedback control input, and relevant sufficient conditions for the existence of the controller are obtained. Because of the suitable choice of state variables, the proposed control strategies can cope with the load uncertainty and have robustness for disturbance. Finally, simulations are carried out via Matlab/Simulink soft to verify the effectiveness of the proposed control strategies. The performance of the proposed control strategies are demonstrated by the simulation results.      

A generalized negative imaginary lemma and Riccati-based static state-feedback negative imaginary synthesis

In this paper, we present a generalized negative imaginary lemma based on a generalized negative imaginary system definition. Then, an algebraic Riccati equation method is given to determine if a system is negative imaginary. Also, a state feedback control procedure is presented that stabilizes an uncertain system and leads to the satisfaction of the negative imaginary property. The controller synthesis procedure is based on the proposed negative imaginary lemma. Using this procedure, the closed-loop system can be guaranteed to be robustly stable against any strict negative imaginary uncertainty, such as in the case of unmodeled spill-over dynamics in a lightly damped flexible structure. A numerical example is presented to illustrate the usefulness of the results.     

A spatial decomposition of the shift-share components of labour productivity inequality in Italy

This paper explores the components of aggregate labour productivity inequality between Italian regions from 2000 to 2013. The Gini index of inequality in aggregate labour productivity is decomposed, showing the extent to which sector productivity differentials and differences in industry-mix contribute to regional productivity inequality. In addition, the contribution of the interaction between differences in industry-mix and sector productivity differentials is revealed by the decomposition. Each of these contributions to inequality is measured by considering the spatial dimension of regional inequality, since the contributions of inequality between non-neighbouring regions and inequality between neighbouring regions are separated.     

A globally convergent BFGS method for pseudo-monotone variational inequality problems

In this paper, we propose a globally convergent BFGS method to solve Variational Inequality Problems (VIPs). In fact, a globalization technique on the basis of the hyperplane projection method is applied to the BFGS method. The technique, which is independent of any merit function, is applicable for pseudo-monotone problems. The proposed method applies the BFGS direction and tries to reduce the distance of iterates to the solution set. This property, called Fejer monotonicity of iterates with respect to the solution set, is the basis of the convergence analysis. The method applied to pseudo-monotone VIP is globally convergent in the sense that subproblems always have unique solutions, and the sequence of iterates converges to a solution to the problem without any regularity assumption. Finally, some numerical simulations are included to evaluate the efficiency of the proposed algorithm.     

Reduced-order multiple observer for Takagi–Sugeno systems with unknown inputs

The paper discusses a niche area problem — the design of reduced-order multiple observers which can achieve the finite-time state reconstruction for Takagi–Sugeno multiple models with unknown inputs. The new reduced-order multiple observer obtained in this paper is only the second ever designed, the author of this paper continuing his work started one year ago with the introduction of the reduced-order multiple observer concept. The obtaining of the new reduced-order multiple observer is achieved by combining two classical reduced-order observers for linear time-invariant multivariable systems with unknown inputs and a full-order multiple observer for Takagi–Sugeno systems. The main innovative idea behind the design of the reduced-order multiple observer for Takagi–Sugeno systems described by the multiple models is the split of the multiple model into two subsystems: an unknown-input-free subsystem and an unknown-input-depending subsystem. The unknown-input-free subsystem is brought to the form of a standard multiple model and, in this situation, any algorithm to design full-order multiple observers can be used in the design of reduced-order multiple observers. The steps of the design procedure have been summarized and software implemented; then, the validation of the suggested algorithm has been done for two concrete cases associated to the motion of an aircraft during its landing     

Improved results on delay-interval-dependent robust stability criteria for uncertain neutral-type systems with time-varying delays

In this paper, we consider the problem of delay-interval-dependent robust stability and stabilization of a class of linear uncertain neutral-type systems with time-varying delay. By constructing a candidate Lyapunov–Krasovskii functional (LKF), that takes into account the delay-range information appropriately, less conservative robust stability criteria are proposed in terms of linear matrix inequalities (LMIs) to compute the maximum allowable upper bounds (MAUB) for the delay-interval within which the uncertain neutral-type system under consideration remains asymptotically stable. The verifiable stabilizability conditions and memoryless state feedback control design are stated. Finally, numerical examples are also designated to demonstrate the effectiveness and reduced conservatism of the developed results.     

Gronwall inequality for hybrid systems

The Gronwall inequality, a well-known and useful result both for continuous-time and discrete-time signals, is extended to hybrid signals, namely those that combine continuous time and discrete time. An application of the result to establishing a bounded energy bounded state property for hybrid systems with inputs is provided.