Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

Delay-range-dependent Stability Criterion for Interval Time-delay Systems with Nonlinear Perturbations

In this paper, we consider the problem of robust stability for a class of linear systems with interval time-varying delay under nonlinear perturbations using Lyapunov-Krasovskii （LK） functional approach. By partitioning the delay-interval into two segments of equal length, and evaluating the time-derivative of a candidate LK functional in each segment of the delay-interval, a less conservative delay-dependent stability criterion is developed to compute the maximum allowable bound for the delay-range within which the system under consideration remains asymptotically stable. In addition to the delay-bi-segmentation analysis procedure, the reduction in conservatism of the proposed delay-dependent stability criterion over recently reported results is also attributed to the fact that the time-derivative of the LK functional is bounded tightly using a newly proposed bounding condition without neglecting any useful terms in the delay-dependent stability analysis. The analysis, subsequently, yields a stable condition in convex linear matrix inequality （LMI） framework that can be solved non-conservatively at boundary conditions using standard numerical packages. Furthermore, as the number of decision variables involved in the proposed stability criterion is less, the criterion is computationally more effective. The effectiveness of the proposed stability criterion is validated through some standard numerical examples.

LESO-based Position Synchronization Control for Networked Multi-Axis Servo Systems With Time-Varying Delay

The position synchronization control(PSC) problem is studied for networked multi-axis servo systems(NMASSs) with time-varying delay that is smaller than one sampling period. To improve the control performance of the system, time-varying delays, modeling uncertainties, and external disturbances are first modeled as a lumped disturbance. Then, a linear extended state observer(LESO) is devised to estimate the system state and the lumped disturbance, and a linear feedback controller with disturbance compensation is designed to perform individual-axis tracking control. After that, a cross-coupled control approach is used to further improve synchronization performance. The bounded-input-bounded-output(BIBO) stability of the closedloop control system is analyzed. Finally, both simulation and experiment are carried out to demonstrate the effectiveness of the proposed method.

Robust asymptotic stability for BAM neural networks with time-varying delays via LMI approach

Several novel stability conditions for BAM neural networks with time-varying delays are studied.Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach,the delay-dependent linear matrix inequality（LMI） conditions are established to guarantee robust asymptotic stability for given delayed BAM neural networks.These criteria can be easily verified by utilizing the recently developed algorithms for solving LMIs.A numerical example is provided to demonstrate the effectiveness and less conservatism of the main results.

Robust fault detection for delta operator switched fuzzy systems with bilateral packet losses

Considering packet losses, time-varying delay, and parameter uncertainty in the switched fuzzy system, this paper designs a robust fault detection filter at any switching rate and analyzes the H∞ performance of the system. Firstly, the Takagi-Sugeno(T-S) fuzzy model is used to establish a global fuzzy model for the uncertain nonlinear time-delay switched system,and the packet loss process is modeled as a mathematical model satisfying Bernoulli distribution. Secondly, through the average dwell time method and multiple Lyapunov functions, the exponentially stable condition of the nonlinear network switched system is given. Finally, specific parameters of the robust fault detection filter can be obtained by solving linear matrix inequalities(LMIs). The effectiveness of the method is verified by simulation results.

Global exponential p-norm stability of BAM neural networks with unbounded time-varying delays:A method based on the representation of solutions

This paper studies the global exponential p-norm stability of bidirectional associative memory(BAM)neural networks with unbounded time-varying delays.A novel method based on the representation of solutions is put forward to deduce a global exponential p-norm stability criterion.This method does not need to set up any Lyapunov-Krasovskii functionals(LKF),which can greatly reduce a large amount of computations and is simpler than the existing methods.In the end,representative numerical examples are given to llustrate the availability of the method.

On Improved Delay-dependent Robust Stability Criteria for Uncertain Systems with Interval Time-varying Delay

This paper considers the problem of delay-dependent robust stability for uncertain systems with interval time-varying delays. By using the direct Lyapunov method, a new Lyapunov-Krasovskii(L-K) functional is introduced based on decomposition approach, when dealing with the time derivative of L-K functional, a new tight integral inequality is adopted for bounding the cross terms. Then, a new less conservative delay-dependent stability criterion is formulated in terms of linear matrix inequalities(LMIs),which can be easily solved by optimization algorithms. Numerical examples are given to show the effectiveness and the benefits of the proposed method.

Predictive Control of High-Order Fully Actuated Nonlinear Systems with Time-Varying Delays

This paper investigates the control problem of high-order fully actuated nonlinear systems with time-varying delays in the discrete-time domain.To make the compensation for time-varying delays concise,active and universal,a novel nonlinear predictive control method is proposed.The designed nonlinear predictive controller can achieve the same expected control performance as the nonlinear systems without delays.At the same time,the necessary and sufficient conditions for the stability of the closed-loop nonlinear predictive control systems are derived.Numerical examples show that the proposed nonlinear predictive controller design method can completely compensate for the time-varying delays of nonlinear systems.

H_∞ FILTERING FOR CONTINUOUS-TIME SYSTEMS WITH POINTWISE TIME-VARYING DELAY

The problem of H∞ filtering for continuous-time systems with pointwise time-varying delay is investigated in this paper. By applying an innovation analysis in Krein space, a necessary and sufficient condition for the existence of an H∞ filter is derived in two methods： One is the partial differential equation approach, the other is the reorganized innovation analysis approach. The former gives a solution to the proposed H∞ filtering problem in terms of the solution of a partial differential equation with boundary conditions. The later gives an analytical solution to the proposed H∞ filtering problem in terms of the solutions of Riccati and matrix differential equations.