ASYMPTOTIC BEHAVIOURS OF STOCHASTIC DIFFERENTIAL DELAY EQUATIONS

Most of the existing results on stochastic stability use a single Lyapunov function, but we shall instead use multiple Lyapunov functions in this paper. We shall establish the sufficient condition, in terms of multiple Lyapunov functions, for the asymptotic behaviours of solutions of stochastic differential delay equations. Moreover, from them follow many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in applications. In particular, the well‐known classical theorem on stochastic asymptotic stability is a special case of our more general results. These show clearly the power of our new results. Two examples are also given for illustration.     

Links between asymptotic controllability and persistence of excitation for a class of time-varying systems

For a class of nonlinear time-varying parameterized systems we prove that persistence of excitation implies global asymptotic controllability to the equilibrium with respect to a set of parameters. The result is used to derive sufficient conditions for global asymptotic controllability for composite systems.     

Asymptotic behavior of morphological filters

The connection between morphological and stack filters is used in the analysis of the statistical properties of morphological filters. Closed-form expressions for the output distributions of morphological filters are given, and their statistical symmetry properties are analyzed. Asytotically tight bounds on the expectations of two-dimensional morphological filters, and asymptotic formulas for the variances of one-dimensional morphological filters are derived. These results form the basis for analyzing general asymptotic properties of morphological filters.     

On a Modification of the PID Controller

In this article we propose a modification of the PID controller. Theexpression for static error for systems with a modified controller isderived. We have obtained the parametric equations describing the boundariesof the asymptotic stability domain in the space of feedback gains. Theasymptotic stability domain for the system of second order with modifiedcontroller is derived. Some numerical results and example arepresented.     

Dynamic control and motion planning technique for a class of nonlinear systems with drift

The paper addresses the synthesis of a smooth dynamic feedback for a class of nonholonomic systems (nonlinear systems with drift). The proposed technique provides asymptotic stability and convergence to a desired equilibrium manifold. The manifold is a (task) function of the generalized co-ordinates. Applications of the proposed technique to control of two classes of nonholonomic systems are presented.     

New Linear Program Performance Bounds for Closed Queueing Networks

We develop new linear program performance bounds for closed reentrantqueueing networks based on an inequality relaxation of the averagecost equation. The approach exploits the fact that the transitionprobabilities under certain policies of closed queueing networksare invariant within certain regions of the state space. Thisinvariance suggests the use of a piecewise quadratic functionas a surrogate for the differential cost function. The linearprogramming throughput bounds obtained are provably tighter thanpreviously known bounds at the cost of increased computationalcomplexity. Functional throughput bounds parameterized by thefixed customer population N are obtained, alongwith a bound on the limiting throughput as N + .We show that one may obtain reduced complexity bounds while stillretaining superiority.     

Unified stabilizing controller synthesis approach for discrete-time intelligent systems with time delays by dynamic output feedback

A novel model, termed the standard neural network model (SNNM), is advanced to describe some delayed (or non-delayed) discrete-time intelligent systems com- posed of neural networks and Takagi and Sugeno (T-S) fuzzy models. The SNNM is composed of a discrete-time linear dynamic system and a bounded static nonlinear operator. Based on the global asymptotic stability analysis of the SNNMs, linear and nonlinear dynamic output feedback controllers are designed for the SNNMs to stabilize the closed-loop systems, respectively. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. Most neural-network-based (or fuzzy) discrete-time intelligent systems with time delays or without time delays can be transformed into the SNNMs for controller synthesis in a unified way. Three application examples show that the SNNMs not only make controller synthesis of neural-network-based (or fuzzy) discrete-time intelligent systems much easier, but also provide a new approach to the synthesis of the controllers for the other type of nonlinear systems.     

Normality evaluations and their relation to personality traits and well-being.

Despite frequent discussions of what it means to be normal in clinical, social, and personality psychology theory, the characteristics of individuals who call themselves normal are little understood. In 5 studies, the authors investigated various hypotheses concerning the nature of normality evaluations. The authors add to recent evidence that normality evaluations represent a distinct dimension of evaluative judgments, showing self-judgments of being normal (versus strange) to be relatively independent from self-judgments of being average (versus unique). Normality evaluations showed positive relations with communal traits such as agreeableness, conscientiousness, and emotional stability, and were negatively related to openness to experience. Supporting a broader hypothesis that normality evaluations may be involved in directing or motivating personality development processes, normality evaluations were positively associated with well-being and a sense of fitting in with one's peers, and individuals who felt abnormal felt a heightened sense that they needed to improve their personality. Finally, the personality correlates of normality evaluations were found to change over the lifespan, largely in parallel with the actual mean-level development of personality traits with age. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Asymptotic normality of the Nadaraya–Watson semivariogram estimators

In this work, the Nadaraya–Watson semivariogram estimation is considered for both the isotropic and the anisotropic settings. Several properties of these estimators are analyzed and, particularly, their asymptotic normality is established in terms of unknown characteristics of the random process. The latter provides a theoretical procedure for construction of confidence intervals for the semivariogram via the normal quantiles, which in practice must be appropriately estimated. A numerical study is included to illustrate the performance of the Nadaraya–Watson estimation when used to obtain confidence intervals.      

Robust global stabilisability by means of sampled-data control with positive sampling rate

This work proposes a notion of robust reachability of one set from another set under constant control. This notion is used to construct a control strategy, involving sequential set-to-set reachability, which guarantees robust global stabilisation of non-linear sampled data systems with positive sampling rate. Sufficient conditions for robust reachability of one set from another under constant control are also provided. The proposed method is illustrated through a number of examples, including the study of the sampled-data stabilisation problem of the chemostat.