Robust Stability of a Class of Uncertain Lur'e Systems of Neutral Type

This paper deals with the problem of stability for a class of Lur’e systems with interval time-varying delay and sector-bounded nonlinearity. The interval time-varying delay function is not assumed to be differentiable. We analyze the global exponential stability for uncertain neutral and Lur’e dynamical systems with some sector conditions. By constructing a set of improved Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, we establish some stability criteria in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the results

Multiadaptive Galerkin Methods for ODEs III: A Priori Error Estimates

The multiadaptive continuous/discontinuous Galerkin methods mcG(q) and mdG(q) for the numerical solution of initial value problems for ordinary differential equations are based on piecewise polynomial approximation of degree q on partitions in time with time steps which may vary for different components of the computed solution. In this paper, we prove general order a priori error estimates for the mcG(q) and mdG(q) methods. To prove the error estimates, we represent the error in terms of a discrete dual solution and the residual of an interpolant of the exact solution. The estimates then follow from interpolation estimates, together with stability estimates for the discrete dual solution

Characterization of Bacillus species exhibiting strong proteolytic activity isolated from Thua Nao

In this study, two bacilli strains, namely TN51 and TN69, previously isolated from Thua Nao, a Thai traditional fermented soybean, were studied in terms of their phenotypic and biochemical properties. Initially, both strains were subjected to morphological determination and a series of biochemical tests. Both were Gram-positive, endosporeforming bacilli. Based on 16S rRNA gene sequence analysis, the identities of strains TN51 and TN69 were confirmed as Bacillus subtilis and B. cereus, respectively. In addition, these two strains were also assessed for their antibiogram profiles. It was found that both strains were susceptible to chloramphenicol, erythromycin, kanamycin, tetracycline, and vancomycin and resistant to ampicillin and intermediately susceptible to bacitracin

Delay-Dependent Guaranteed Cost Controller Design for Uncertain Neural Networks with Interval Time-Varying Delay

This paper studies the problem of guaranteed cost control for a class of uncertain delayed neural networks. The time delay is a continuous function belonging to a given interval but not necessary to be differentiable. A cost function is considered as a nonlinear performance measure for the closed-loop system. The stabilizing controllers to be designed must satisfy some exponential stability constraints on the closed-loop poles. By constructing a set of augmented Lyapunov-Krasovskii functionals combined with Newton-Leibniz formula, a guaranteed cost controller is designed via memoryless state feedback control, and new sufficient conditions for the existence of the guaranteed cost state feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result

Exponentially practical stability of discrete time singular system with delay and disturbance

Abstract In this paper, we consider exponentially practical stability of a discrete time singular system with disturbance. By using Lyapunov–Krasovskii stability theory, some criteria for exponentially practical stability of such a system are derived. Moreover, by using a Razumikhin-type technique, the criteria for exponentially practical stability of a discrete time singular system with delay and disturbance are also obtained. Some numerical examples are given to show the success of our theoretical results

H∞ Control for Nonlinear Systems with Time-Varying Delay Using Matrix-Based Quadratic Convex Approach

H∞ control problem for nonlinear system with time-varying delay is considered by using a set of improved Lyapunov-Krasovskii functionals including some integral terms, and a matrix-based on quadratic convex, combined with Wirtinger's inequalities and some useful integral inequality. H∞ controller is designed via memoryless state feedback control and new sufficient conditions for the existence of the H∞ state feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result

New Results on Robust Stability and Stabilization of Linear Discrete-Time Stochastic Systems with Convex Polytopic Uncertainties

This paper addresses the robust stability for a class of linear discrete-time stochastic systems with convex polytopic uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of linear discrete-time stochastic control systems is given. Numerical examples are included to illustrate the effectiveness of our results

New Results on Robust Stability and Stabilization of Linear Discrete-Time Stochastic Systems with Convex Polytopic Uncertainties

This paper addresses the robust stability for a class of linear discrete-time stochastic systems with convex polytopic uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of linear discrete-time stochastic control systems is given. Numerical examples are included to illustrate the effectiveness of our results