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The problem of existence and stability of equilibria of linear systems with constant power loads is addressed in this paper. First, we correct an unfortunate mistake in our recent paper refid="ref10"/ pertaining to the sufficiency of the condition for existence of equilibria in multiport systems given there. Second, we give two necessary conditions for existence of equilibria. The first one is a simple linear matrix inequality hence it can be easily verified with existing software. Third, we prove that the latter condition is also sufficient if a set defined by the problem data is convex, which is the case for single and two-port systems. Finally, sufficient conditions for stability and instability for a given equilibrium point are given. The results are illustrated with two benchmark examples. [ABSTRACT FROM PUBLISHER]

This paper develops a neural network for solving the general nonsmooth convex optimization problems. The proposed neural network is modeled by a differential inclusion. Compared with the existing neural networks for solving nonsmooth convex optimization problems, this neural network has a wider domain for implementation. Under a suitable assumption on the constraint set, it is proved that for a given nonsmooth convex optimization problem and sufficiently large penalty parameters, any trajectory of the neural network can reach the feasible region in finite time and stays there thereafter. Moreover, we can prove that the trajectory of the neural network constructed by a differential inclusion and with arbitrarily given initial value, converges to the set consisting of the equilibrium points of the neural network, whose elements are all the optimal solutions of the primal constrained optimization problem. In particular, we give the condition that the equilibrium point set of the neural network coincides with the optimal solution set of the primal constrained optimization problem and the condition ensuring convergence to the optimal solution set in finite time. Furthermore, illustrative examples show the correctness of the results in this paper, and the good performance of the proposed neural network. [ABSTRACT FROM AUTHOR]

Multistable networks have attracted much interest in recent years, since multistability is of primary importance for some applications of recurrent neural networks where monostability exhibits some restrictions. This paper focuses on the analysis of dynamical property for a class of additive recurrent neural networks with nonsaturating linear threshold transfer functions. A milder condition is derived to guarantee the boundedness and global attractivity of the networks as compared to that presented in [6]. Dynamical properties of the equilibria of two-dimensional networks are analyzed theoretically, and the relationships between the equilibria features and network parameters (synaptic weights and external inputs) are revealed. In addition, the sufficient and necessary conditions for coexistence of multiple equilibria are obtained, which confirmed the observations in [14] with a cortex-inspired silicon circuit. The results obtained in this paper are applicable to both symmetric and nonsymmetric networks. Simulation examples are used to illustrate the theory developed in this paper. [ABSTRACT FROM AUTHOR]

Dichotomy, or monostability, is one of the most important properties of nonlinear dynamic systems. For a dichotomous system, the solution of the system is either unbounded or convergent to a certain equilibrium, thus periodic or chaotic states cannot exist in the system. In this paper, a new methodology for the analysis of dichotomy of a class of nonlinear systems is proposed, and a linear matrix inequality (LMI)-based criterion is derived. The results are then extended to uncertain systems with real convex poly- topic uncertainties in the linear part, and the LMI representation for robust dichotomy allows the use of parameter-dependent Lyapunov function. Based on the results, a dynamic output feedback controller guaranteeing robust dichotomy is designed, and the controller parameters are explicitly expressed by a set of feasible solutions of corresponding linear matrix inequalities. An extended Chua's circuit with two nonlinear resistors is given at the end of the paper to demonstrate the validity and applicability of the proposed approach. It is shown that by investigating the convergence of the bounded oscillating solutions of the system, our results suggests a viable and effective way for chaos control in nonlinear circuits. [ABSTRACT FROM AUTHOR]

In this paper we combine partial stability and set invariance methods, which is a necessary development for applications such as synchronization. We use set invariance methods to ensure that the ‘auxiliary’ variables remain on a restricted domain, and then use this framework to develop new results for both local and global partial stability theory. We apply the methodology to identical synchronization of oscillator networks, which gives rigorous conditions for existing local methodology as well as novel global methodology. The work also allows a common framework for synchronization analysis of both oscillator networks and power systems. We show the applicability by finding novel synchronization conditions for an example oscillator network. [ABSTRACT FROM PUBLISHER]

In this paper, we first introduce the model of single-driving double-response system (SDDRS), which consists of a driving system (subsystem) and two response systems (sub- systems). By applying the theory of Lyapunov stability, we study the projective synchronization of SDDRS between the driving and response systems. The sufficient conditions for achieving projec- tive synchronization are obtained when the driving system has either a globally stable equilibrium point or a chaotic attractor. Furthermore, we use the SDDRS for cryptography in secure communication and present a novel scheme for encryption and decryption based on its projection synchronization. The results of numerical simulations verify the efficiency of the presented control schemes and the excellence of cryptography. [ABSTRACT FROM AUTHOR]

In this paper, we study the Cohen-Grossberg neural networks with discrete and distributed delays. For a general class of internal decay functions, without assuming the boundedness, differentiability, and monotonicity of the activation functions, we establish some sufficient conditions for the existence of a unique equilibrium and its global asymptotic stability. Theory of M-matrices and Lyapunov functional technique are employed. The criteria are independent of delays and hence delays are harmless in our case. Our results improve and generalize some existing ones. [ABSTRACT FROM AUTHOR]

Modeling single-machine (synchronous-generator) infinite-bus (SMIB) systems with what we call the improved swing equations is considered in this paper. The existence and properties of local solutions to the improved swing equations are then examined. Furthermore, the local stability of the SMIB systems is scrutinized. By interpreting the improved swing equations with Taylor expansions, approximate linear time-invariant improved swing equations are derived, with which the dynamics of the SMIB systems can be estimated pointwisely. Comparisons between the improved and conventional swing equations are made through illustrative examples. [ABSTRACT FROM AUTHOR]

The 555 timer IC is a well-known integrated circuit having been widely used as a pulse generator. We propose a circuit containing a single 555 IC, an LED, an inductor, two capacitors, and three resistors that exhibits chaos. The IC serves as a hysteretic switch causing the system to be alternately attracted to each of two stable equilibria. Ours appears to be the first chaotic circuit governed by piecewise-linear equations that have stable but no unstable equilibria. Also unique is the sensitive dependence on initial conditions resulting only from a square-root map. This arises from the grazing impact of two voltages. The circuit is also unusual in exhibiting periodic orbits with a Farey tree structure and a transition to chaos via a period-adding cascade. This and other bifurcations seen experimentally are in agreement with those of the governing three-dimensional ODEs with hysteretic conditions. Inclusion of three extra resistors in the circuit lowers the characteristic frequency so that the bifurcations can be detected via the LED without the need of an oscilloscope. The circuit is therefore also suitable for experimentation by electronics hobbyists with limited resources. [ABSTRACT FROM AUTHOR]

Dynamic security region (DSR) for security assessment and preventive control is defined in terms of variables that are under the control of the dispatcher prior to a fault. The boundary of DSR can be expressed using the function describing the stable manifold of the controlling unstable equilibrium point. The function is shown to be the solution of a partial differential equation. Quadratic and linear approximations to the function characterizing the boundary of DSR are derived. Numerical tests of the approximations are conducted. Potential applications of the method are discussed. [ABSTRACT FROM AUTHOR]

A new dynamical system and computational circuit is described and analyzed. The dynamics permits the construction of a Lyapunov function that ensures global convergence to a unique stable equilibrium. The analog circuit realization is of the neural network type, with N cells represented by high-gain amplifiers, global feedback, and at most 2N interconnections, where N is the number of inputs. A specific application (called "the K-selector") which signals the ranks of the K largest elements of input list and, in parallel the rank of the (K + 1)th element, is designed and numerically tested. For a given density of the input elements, one obtains feasible separation intervals of output signals, i.e., good processing performances. The circuit requires an appropriate control source and suitable scaling of the input data. [ABSTRACT FROM AUTHOR]

Cellular neural networks (CNNs) are dynamical systems, described by a large set of coupled nonlinear differential equations. The equilibrium-point analysis is an important step for understanding the global dynamics and for providing design rules. We yield a set of sufficient conditions (and a simple algorithm for checking them) ensuring the existence of at least one stable equilibrium point. Such conditions give rise to simple constraints, that extend the class of CNNs, for which the existence of a stable equilibrium point is rigorously proved. In addition, they are suitable for design and easy to check, because they are directly expressed in term of the template elements. [ABSTRACT FROM AUTHOR]