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We construct a generic, simple, and efficient scheduling policy for stochastic processing networks, and provide a general framework to establish its stability. Our policy is randomized and prioritized: with high [...]

We consider the use of importance sampling to compute expectations of functionals of Markov processes. For a class of expectations that can be characterized as positive solutions to a linear [...]

We study the long-term behavior of the optimal harvesting policies for a mixed forest composed by multiple species of different maturity ages. This model is a prototype for the exploitation [...]

This paper develops a Lyapunov approach for studying convergence and stability of a class of differential inclusions termed differential variational inequalities (DVIs). The DVIs describe the dynamics of a general system evolving in a compact convex subset of the state space. In particular, they include the dynamics of the full-range (FR) model of cellular neural networks (CNNs), which is characterized by hard-limiter nonlinearities with vertical segments in the i--v characteristic. The approach is based on the following two main tools: 1) a set-valued derivative, which enables to compute the evolution of a Lyapunov function along the solutions of the DVIs without involving integrations, and 2) an extended version of LaSalle's invariance principle, which permits to study the limiting behavior of the solutions with respect to the invariant sets of the DVIs. Then, this paper establishes conditions for convergence (complete stability) of DVIs in the presence of multiple equilibrium points (EPs), global asymptotic stability (GAS), and global exponential stability (GES) of the unique EP. These conditions are applied to investigate convergence, GAS, and GES for FR-CNNs and some extended classes of FR-CNNs. It is shown that, by means of the techniques developed in this paper, the analysis of convergence and stability of FR-CNNs is no more difficult than that of the standard (S)-CNNs. In addition, there are significant cases, such as the symmetric FR-CNNs and the nonsymmetric FR-CNNs with a Lyapunov diagonally stable matrix, where the proof of convergence or global stability is much simpler than that of the S-CNNs. Index Terms--Cellular neural networks (CNNs), convergence, differential variational inequalities (DVIs), full-range (FR) model, LaSalle's invariance principle, set-valued derivative.

This brief addresses the global asymptotic stability (GAS) of delayed neural networks. Based on the Lyapunov method, using some existing results for the existence and uniqueness of the equilibrium point, some sufficient conditions are obtained for checking the GAS without demanding the boundedness and differentiability hypotheses for activation functions. Through comparison, it is illustrated that our conditions extend and improve some recent results. Index Terms--Delayed neural networks, equilibrium point, global asymptotic stability (GAS), Lyapunov functional.

This brief presents a very low complexity hardware interleaver implementation for turbo code in wideband CDMA (W-CDMA) systems. Algorithmic transformations are extensively exploited to reduce the computation complexity and latency. Novel VLSI architectures are developed. The hardware implementation results show that an entire turbo interleave pattern generation unit consumes only 4 k gates, which is an order of magnitude smaller than conventional designs. Index Terms--CDMA, interleaver, turbo codes, VLSI architecture.

This brief studies uncertain discrete impulsive systems. The robustly asymptotical stability criteria are established for linear discrete impulsive system and a class of uncertain nonlinear discrete impulsive systems, respectively. These stability criteria are expressed in terms of fairly simple algebraic conditions so that they are easy to be tested. Some examples are given to illustrate results obtained by us. Index Terms--Discrete impulsive system, Lyapunov function, robustly asymptotical stability, uncertainty.

In this brief, we propose a method of synthesizing a model predictive control (MPC) law for linear parameter varying systems. The proposed method is derived by using the parameter dependent Lyapunov function. The proposed MPC algorithm is reduced to the linear matrix inequality problem. It is shown that the proposed control method achieves less conservative results as compared with the several existing methods. A numerical example is provided to illustrate effectiveness of the proposed method. Index Terms--Linear matrix inequality (LMI), linear parameter varying (LPV) system, model predictive control (MPC), parameter dependent Lyapunov function (PDLF).

An efficient and yet simple neural-based approach is utilized to design real finite-impulse response filters with arbitrary complex frequency responses in the least-squares sense. The proposed approach establishes the quadratic error difference of the filter optimization in the frequency domain as the Lyapunov energy function. Consequently, the optimal filter coefficients are obtained with good performance and fast convergence speed. To achieve good convergences for large filter lengths, a cooling process of simulated annealing is used for the neural activation function. Several examples and comparisons to the existing methods are presented to illustrate the effectiveness and flexibility of the neural-based method. Index Terms--Finite-impulse response (FIR) filter, Lyapunov energy function, neural network, real-time processing.

This brief studies the adaptive robust stabilization problem for nonlinear systems in output feedback form with the high-frequency gain sign unknown. The problem is solved by integrating the robust control method and the Nussbaum gain technique. Also, we show that the celebrated Chua's circuit is a nonlinear system in output feedback form, and apply our approach to design a control law to achieve global stability of the closed-loop system in the presence of uncertain parameters and unknown high-frequency gain sign. Index Terms--Control theory, Lyapunov methods, nonlinear systems, stability.

We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all continuous-time subsystems are Hurwitz stable, all discrete-time subsystems are Schur stable, and furthermore the obtained Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. A numerical example is provided to demonstrate the result. Index Terms--Arbitrary switching, common quadratic Lyapunov functions, continuous-time, discrete-time, exponential stability, Lie algebra, switched systems.

In this paper, a new scheme based on integral observer approach is designed for a class of chaotic systems to achieve synchronization. Unlike the proportional observer approach, the proposed scheme is demonstrated to be effective under a noisy environment in the transmission channel. Based on the Lyapunov stability theory, a sufficient condition for synchronization is derived in the form of a Lyapunov inequality. This Lyapunov inequality is further transformed into a linear matrix inequality (LMI) form by using the Schur theorem and some matrix operation techniques, which can be easily solved by the LMI toolboxes for the design of suitable control gains. It is demonstrated with the Murali-Lakshmanan-Chua system that a better noise suppression and a faster convergence speed can be achieved for chaos synchronization by using this integral observer scheme, as compared with the traditional proportional observer approach. Index Terms--Chaos synchronization, disturbance, integral observer, linear matrix inequality, Lyapunov stability theory.

We consider a switching system composed of a finite number of linear delay differential equations (DDEs). It has been shown that the stability of a switching system composed of a finite number of linear ordinary differential equations (ODEs) may be achieved by using a common Lyapunov function method switching rule. We modify this switching rule for ODE systems to a common Lyapunov functional method switching rule for DDE systems and show that it stabilizes our model. Our result uses a Riccati-type Lyapunov functional under a condition on the time delay. Index Terms--Delay differential equations (DDEs), Lyapunov functional, switching systems.

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. Index Terms--Cohen-Grossberg neural network, discrete delay, distributed delay, equilibrium, global (asymptotic) stability, M-matrix.

Global synchronization and asymptotic stability of complex dynamical networks are investigated in this paper. Based on a reference state, a sufficient condition for global synchronization and stability is derived. Unlike other approaches where only local results were obtained, the complex network is not linearized in this paper. Instead, the sufficient condition for the global synchronization and asymptotical stability is obtained here by introducing a reference state with the Lyapunov stability theorem rather than the Lyapunov exponents, and this condition is simply given in terms of the network coupling matrix therefore is very convenient to use. Furthermore, the developed technique is applied to networks consisting of nodes with unknown but bounded nonlinear functions. A typical example of a complex network with chaotic nodes is finally used to verify the theoretical results and the effectiveness of the proposed synchronization scheme. Index Terms--Asymptotic stability, chaos, complex network, global synchronization.

Exact nonlinear differential equations of boost pulsewidth modulation converters (either with hard-switching or soft-switching, in continuous and discontinuous conduction mode) are obtained, without using average approximations. An extended system of equations also contains the differential equation of the integrated error between the reference and the output voltage. A positive-definite Lyapunov function is defined, including in its expression a nonlinear integral of type Lurie. Sufficient conditions for the Lyapunov stability of the system are determined. Consequently, constraints on the feedback circuit parameters that assure the large-signal stability of the system are formulated. These constraints relate the parameters of the feedback circuit with the values of the power stage elements, load, switching frequency, steady-state duty-cycle. For different values of the steady-state duty-cycle, graphical boundaries which assure the large-signal stability for all the variation of the load are designed. Simulations and experiments confirm the stability of the design. Index Terms--Boost regulator, large-signal stability, Lyapunov stability.

In a recent paper on semidefinite linear complementarity problems, Gowda and Song (2000) introduced and studied the P-property, [P.sub.2]-property, GUS-property, and strong monotonicity property for linear transformation L: [S.sup.n] → [...]

This paper is devoted to stability analysis of linear systems with state delay and input saturation. The domain of attraction resulting from an a priori designed state feedback law is analyzed using Lyapunov-Razumikhin and Lyapunov-Krasovskii functional approach. Both delay-independent and delay-dependent estimation of the domain of attraction are presented using the linear matrix inequality technique. The problem of designing linear state feedback laws such that the domain of attraction is enlarged is formulated and solved as an optimization problem with LMI constraints. Numerical examples are used to demonstrate the effectiveness of the proposed design technique. Index Terms--Actuator saturation, domain of attraction, linear matrix inequality, time-delay.

In this paper, a simple and systematic control design method is proposed for a discrete-time Takagi-Sugeno (TS) fuzzy system, which employs the parallel distributed compensation (PDC) to determine the structure of a fuzzy controller so as to make all the Lyapunov exponents of the controlled TS fuzzy system strictly positive. This approach is proven to be mathematically rigorous for anticontrol of chaos for a TS fuzzy system, in the sense that any given discrete-time TS fuzzy system can be made chaotic by the designed PDC controller along with the mod-operation. A numerical example is included to visualize the anticontrol effect. Index Terms--Anticontrol of chaos, Lyapunov exponents, parallel distributed compensation (PDC), TS fuzzy system.

This paper presents controller design and analysis methods for uncertain piecewise-linear systems based on a piecewise-smooth Lyapunov function. The basic idea of the proposed approaches is to construct controllers for the uncertain piecewise-linear systems in such a way that a piecewise-continuous Lyapunov function can be used to establish the global stability or the global stability with [H.sub.[infinity]] performance of the resulting closed loop control systems. It is shown that the control laws can be obtained by solving a set of linear matrix inequalities (LMI) that are numerically feasible with commercially available software. An example is given to illustrate the application of the proposed methods. Index Terms--Controller design, [H.sub.[infinity]] control, linear matrix inequality, piecewise-linear systems.

In this tutorial paper, various phenomena linked to the synchronization of chaotic systems are discussed using the simple example of two coupled skew tent maps. The phenomenon of locally riddled basins of attraction is explained using the Lyapunov exponents transversal to the synchronization manifold. The skew tent maps are coupled in two different ways, leading to quite different global dynamic behavior especially when the ideal system is perturbed by parameter mismatch or noise. The linear coupling leads to intermittent desynchronization bursts of large amplitude, whereas for the nonlinear coupling the synchronization error is asymptotically uniformly bounded. Index Terms - Chaos, Lyapunov exponents, nonlinear systems, synchronization.

The stability and instability of fluid models are analyzed in consideration of Dai's (1995) recently introduced theorem stating that the stability of a scheduling policy depends on the stability of the corresponding fluid model. The study uses the piecewise linear Lyapunov functions introduced by Botvitch and Zamyatin (1992). The stability of First-Buffer-First-Served and Last-Buffer-First-Served disciplines is determined in all reentrant lines. The stability of the Lu and Kumar's four buffer network and of Kelly-type networks is also established.

This paper describes an approach to the stability analysis of two-dimensional (2-D) digital filters that are modeled in the Fornasini-Marchesini state space using a class of generalized 2-D Lyapunov equations. The generalization was made based on the constant 2-D Lyapunov equation proposed recently by Hinamoto. It is shown that the use of the generalize Lyapunov equations narrows the gap between 'sufficiency' and 'necessity' for a state-space digital filter to be stable, which occurs in Hinamoto's Lyapunov theorem. Feasible methods for finding numerical solutions of the generalized 2-D Lyapunov equation are also proposed. An example is included to illustrate the main results of the paper.

This paper has three contributions. The first involves polytopes of matrices whose characteristic polynomials also lie in a polytopic set (e.g. companion matrices). We show that this set is Hurwitz or Schur invariant iff there exist multiaffinely parameterized positive definite, Lyapunov matrices that solve an augmented Lyapunov equation. The second result concerns uncertain transfer functions with denominator and numerator belonging to a polytopic set. We show all members of this set are strictly positive real if the Lyapunov matrices solving the equations featuring in the Kalman-Yakubovic-Popov Lemma are multiaffinely parameterized. Moreover, under an alternative characterization of the underlying polytopic sets, the Lyapunov matrices for both of these results admit affine parameterizations. Finally, we apply the Lyapunov equation results to derive stability conditions for a class of linear time varying systems.

Sufficient conditions for the global asymptotic stability of the equilibrium [x.sub.e] = 0 of discrete-time dynamical systems which have saturation nonlinearities on part of the states are established. We utilize a class of positive definite and radially unbounded Lyapunov functions in establishing our results. When using quadratic form Lyapunov functions, our results involve necessary and sufficient conditions under which positive definite matrices can be used to generate Lyapunov functions for the systems considered herein.

A stability criterion for uncertain systems with time-varying delay is derived via the Lyapunov functional approach. By checking the Hamiltonian matrix and solving an algebraic Riccati equation, a new bound on allowable stability preserving nonlinear perturbations is presented. The result obtained here is shown to be less conservative than others reported in the literature. Index Terms--Robust stability, time-delay systems, uncertain systems.

A one-dimensional iterative chaotic map with infinite collapses within symmetrical region [-1, 0) [union] (0, +1] is proposed. The stability of fixed points and that around the singular point are analyzed. Higher Lyapunov exponents of proposed map show stronger chaotic characteristics than some iterative and continuous chaotic models usually used. There exist inverse bifurcation phenomena and special main periodic windows at certain positions shown in the bifurcation diagram, which can explain the generation mechanism of chaos. The chaotic model with good properties can be generated if choosing the parameter of the map properly. Stronger inner pseudorandom characteristics can also be observed through [chi square] test on the supposition of even distribution. This chaotic model may have many advantages in practical use. Index Terms--Bifurcation, iterative chaotic map with infinite collapses, Lyapunov exponents, main periodic windows, stability, [chi square] test.

In this brief, an adaptive chaos control method is developed for stabilizing chaotic systems at their unknown equilibrium(s) using the invariant manifold theory. The developed method overcomes the problem that the equilibrium(s) of the chaotic systems are dependent on the unknown system parameters, which makes direct application of the conventional adaptive control difficult. Further development of the adaptive chaos control is undertaken for the situation where the parameter estimates are only allowed to vary within a bounded set due to the sensitivity of chaotic systems to parameter variations. A sufficient condition for convergence of system states and parameter estimates is obtained. The design method developed then is applied to stabilizing the Lorenz chaotic system at an unknown equilibrium. Both mathematical and computational results have demonstrated the effectiveness of this method. Index Terms--Adaptive control, chaos control, invariant manifolds, Lorenz system, Lyapunov method.

This work evolved from an endeavor to derive stability criteria and Poincare normal forms for nonlinear systems associated with a nonsemisimple zero (in Part I) or a pair of imaginary eigenvalues (in Part II). The stability criteria are given in terms of the noninteracting vector restoring and restraining forces, which are motivated from the Lienard equation for nonlinear mass-damper-spring system models. Lyapunov functions are constructed explicitly to fulfill the La Salle invariant principle for local or global stability assertion. It turned out that the Lyapunov functions thus constructed apply to a wide variety of linear stability scenarios. By introducing the notions of restoring and restraining forces, how the Lyapunov functions, the stability criteria and the system dynamics interplay are also exhibited. Two distinct classes of nonlinearities which we refered to as being arithmetical and transcendental, emerged. In some sense, such systems carry nonlinear lags coexisting with the linear lead. In particular, a characteristic of the nonlinear dynamics, a staircase structure, is discovered. Further extension is also made to incorporate nondestabilizing perturbation, which bears important bifurcational implications. Index Terms--Lyapunov function/stability, nonsemisimple zero mode, Poincare normal forms.

This paper studies nonlinear systems associated with or linked to a nonsemisimple (NSS) pair of imaginary eigenvalues. Stability criteria and Poincare normal forms (PNF's) are derived via explicit construction of Lyapunov functions. It is a counterpart and continuation of Part I, which considered the case with an NSS zero eigenvalue. While originating from stability analysis for a nonsemisimple critical mode, the development extends to co-existing (semi-) simple critical modes and to stable modes, as in Part I. The present NSS imaginary pairs (NSSIP) case is shown to possess certain characteristics common to NSS zero (NSSZ), such as the nonlinear lag and the staircase structure, but retains its own identities as well. These include the less surprising, the submodular variable-pair circles which emerge from the units of the potential generator and the more remarkable stricter specification in the dynamics, which is possibly attributable to the inherited conjugacy. An elementary partial differential equation traversing the development shows potential for nontrivial generalization. Index Terms--Lyapunov function/stability, nonsemisimple imaginary pair mode, Poincare normal forms.

This paper considers the stabilization and synchronization of Chua's oscillators via an impulsive control with time-varying impulse intervals. Some less conservative conditions were derived in the sense that the Lyapunov function is only required to be nonincreasing along a subsequence of the switchings. Index Terms--Chua's oscillators, impulsive control, Lyapunov functions, stabilization.

This brief investigates backstepping and adaptive-backstepping design for the control of a class of discrete-time chaotic systems with known or unknown parameters. The proposed method presents a systematic procedure for the control of a class of discrete-time chaotic systems. It can be used for the stabilization of discrete-time chaotic systems to a steady state as well as tracking of any desired trajectory. Moreover, dead-beat control and tracking, exact stabilization at a fixed point and tracking of any desired trajectory in finite time can be achieved. The chaotic Henon system with known or unknown parameters is taken as an example to illustrate the applicability and effectiveness of the backstepping design. Index Terms--Backstepping design, chaos control, Lyapunov function, stabilization, tracking.

In this paper, some novel criteria for the global robust stability of a class of interval Hopfield neural networks with constant delays are given. Based on several new Lyapunov functionals, delay-independent criteria are provided to guarantee the global robust stability of such systems. For conventional Hopfield neural networks with constant delays, some new criteria for their global asymptotic stability are also easily obtained. All the results obtained are generalizations of some recent results reported in the literature for neural networks with constant delays. Numerical examples are also given to show the correctness of our analysis. Index Terms--Interval Hopfield neural networks, Lyapunov functionals, robust stability, time delays.

Based on the Lyapunov stability theorem as well as some facts about the positive definiteness and inequality of matrices, a new sufficient condition is presented for the existence of a unique equilibrium point and its global asymptotic stability of delayed CNNs. This condition imposes constraints on the feedback matrices independent of the delay parameter. This condition is less restrictive than that given in the earlier references. Index Terms--Cellular neural networks, global asymptotic stability, stable equilibrium point.

An approach is proposed for making a given stable continuous-time Takagi-Sugeno (TS) fuzzy-system chaotic, by first discretizing it and then using state feedback control of arbitrarily small magnitude. The feedback controller chosen among several candidates is a simple sinusoidal function of the system states, which can lead to uniformly bounded state vectors of the controlled system with positive Lyapunov exponents, and satisfy the chaotic mechanisms of stretching and folding, thereby yielding chaotic dynamics. This approach is mathematically proven for rigorous generation of chaos from a stable continuous-time TS fuzzy system, where the generated chaos is in the sense of Li and Yorke. A numerical example is included to visualize the theoretical analysis and the controller design.

In this paper a method for robust synthesis of full static-state error feedback and dynamic-output error feedback for master-slave synchronization of Lur'e systems is presented. Parameter mismatch between the systems is considered in the synchronization schemes. Sufficient conditions for uniform synchronization with a bound on the synchronization error are derived, based on a quadratic Lyapunov function. The matrix inequalities from the case without parameter mismatch between the Lur'e systems remain preserved, but an additional robustness criterion must be taken into account. The robustness criterion is based on an uncertainty relation between the synchronization error bound and the parameter mismatch. The robust synthesis method is illustrated on Chua's circuit with the double scroll. One observes that it is possible to synchronize the master-slave systems up to a relatively small error bound, even in the case of different qualitative behavior between the master and the uncontrolled slave system, such as limit cycles and stable equilibria. Index Terms - Chua's circuit, Lur'e systems, matrix inequalities, synchronization.