Delay-dependent robust stability and H_∞ analysis of stochastic systems with time-varying delay

This paper investigates the robust stochastic stability and H∞ analysis for stochastic systems with time-varying delay and Markovian jump. By using the freeweighting matrix technique, i.e., He＇s technique, and a stochastic Lyapunov-Krasovskii functional, new delay-dependent criteria in terms of linear matrix inequalities are derived for the the robust stochastic stability and the H∞ disturbance attenuation. Three numerical examples axe given. The results show that the proposed method is efficient and much less conservative than the existing results in the literature.

Robust Stability Analysis of Edge Polynomials with Variable Length

The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with variable length is characterized in terms of the real spectral radius of the matrix H -1 ( f 0) H (g) , where both H (f 0) and H (g) are Hurwitz like matrices. Based on this result, stability radius of control systems with interval type plants and first order controllers are determined.

Insights into ionic association boosting water oxidation activity and dynamic stability

There have been reports about Fe ions boosting oxygen evolution reaction(OER)activity of Ni-based catalysts in alkaline conditions,while the origin and reason for the enhancement remains elusive.Herein,we attempt to identify the activity improvement and discover that Ni sites act as a host to attract Fe(Ⅲ)to form Fe(Ni)(Ⅲ)binary centres,which serve as the dynamic sites to promote OER activity and stability by cyclical formation of intermediates(Fe(Ⅲ)→Fe(Ni)(Ⅲ)→Fe(Ni)-OH→Fe(Ni)-O→Fe(Ni)OOH→Fe(Ⅲ))at the electrode/electrolyte interface to emit O_(2).Additionally,some ions(Co(Ⅱ),Ni(Ⅱ),and Cr(Ⅲ))can also be the active sites to catalyze the OER process on a variety of electrodes.The Fe(Ⅲ)-catalyzed overall water-splitting electrolyzer comprising bare Ni foam as the anode and Pt/Ni-Mo as the cathode demonstrates robust stability for 1600 h at 1000 mA cm^(-2)@~1.75 V.The results provide insights into the ioncatalyzed effects boosting OER performance.

Nonlinear robust adaptive control for bidirectional stabilization system of all-electric tank with unknown actuator backlash compensation and disturbance estimation

Since backlash nonlinearity is inevitably existing in actuators for bidirectional stabilization system of allelectric tank,it behaves more drastically in high maneuvering environments.In this work,the accurate tracking control for bidirectional stabilization system of moving all-electric tank with actuator backlash and unmodeled disturbance is solved.By utilizing the smooth adaptive backlash inverse model,a nonlinear robust adaptive feedback control scheme is presented.The unknown parameters and unmodelled disturbance are addressed separately through the derived parametric adaptive function and the continuous nonlinear robust term.Because the unknown backlash parameters are updated via adaptive function and the backlash effect can be suppressed successfully by inverse operation,which ensures the system stability.Meanwhile,the system disturbance in the high maneuverable environment can be estimated with the constructed adaptive law online improving the engineering practicality.Finally,Lyapunov-based analysis proves that the developed controller can ensure the tracking error asymptotically converges to zero even with unmodeled disturbance and unknown actuator backlash.Contrast co-simulations and experiments illustrate the advantages of the proposed approach.

Robust Stability and Stabilization of Discrete Singular Systems with Interval Time-varying Delay and Linear Fractional Uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality （LMI） approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.

Robust stability and H-infinity control for uncertain discrete-time Markovian jump singular systems

The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent （r.s.e.） transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality （LMI） conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with 7- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the oaoer.

An improved robust stability and robust stabilization method for linear discrete-time uncertain systems

This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix. Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases. A numerical example illustrates the improvement over the existing ones.

Robust stability analysis of singular linear system with delay and parameter uncertainty

This paper deals with the problem of robust stability for continuous-time singular systems with state delay and parameter uncertainty. The uncertain singular systems with delay considered in this paper are assumed to be regular and impulse free.By decomposing the systems into slow and fast subsystems,a robust delay-dependent asymptotic stability criteria based on linear matrix inequality is proposed, which is derived by using Lyapunov-Krasovskii functionals, neither model transformation nor bounding for cross terms is required in the derivation of our delay-dependent result. The robust delay-dependent stability criterion proposed in this paper is a sufficient condition. Finally, numerical examples and Matlab simulation are provided to illustrate the effectiveness of the proposed method.

Stability analysis and design of time-delay uncertain systems using robust reliability method

A robust reliability method for stability analysis and reliability-based stabilization of time-delay dynamic systems with uncertain but bounded parameters is presented by treating the uncertain parameters as interval variables.The performance function used for robust reliability analysis is defined by a delayindependent stability criterion.The design of robust controllers is carried out by solving a reliability-based optimization problem in which the control cost satisfying design requirements is minimized.This kind of treatment makes it possible to achieve a balance between the reliability and control cost in the design of controller when uncertainties must be taken into account.By the method,a robust reliability measure of the degree of stability of a time-delay uncertain system can be provided,and the maximum robustness bounds of uncertain parameters such that the time-delay system to be stable can be obtained.All the procedures are based on the linear matrix inequality approach and therefore can be carried out conveniently.The effectiveness and feasibility of the proposed method are demonstrated with two practical examples.It is shown by numerical simulations and comparison that it is meaningful to take the robust reliability into account in the control design of uncertain systems.

2-D algebraic test for robust stability of time-delay systems with interval parameters

The robust stability test of time-delay systems with interval parameters can be concluded into the robust stability of the interval quasipolynomials. It has been revealed that the robust stability of the quasipolynomials depends on that of their edge polynomials. This paper transforms the interval quasipolynomials into two-dimensional （2-D） interval polynomials （2-D s-z hybrid polynomials）, proves that the robust stability of interval 2-D polynomials are sufficient for the stability of given quasipolynomials. Thus, the stability test of interval quasipolynomials can be completed in 2-D s-z domain instead of classical 1-D s domain. The 2-D s-z hybrid polynomials should have different forms under the time delay properties of given quasipolynomials. The stability test proposed by the paper constructs an edge test set from Kharitonov vertex polynomials to reduce the number of testing edge polynomials. The 2-D algebraic tests are provided for the stability test of vertex 2-D polynomials and edge 2-D polynomials family. To verify the results of the paper to be correct and valid, the simulations based on proposed results and comparison with other presented results are given.

A new result on global exponential robust stability of neural networks with time-varying delays

In this paper, the global exponential robust stability of neural networks with ume-varying delays is investigated. By using nonnegative matrix theory and the Halanay inequality, a new sufficient condition for global exponential robust stability is presented. It is shown that the obtained result is different from or improves some existing ones reported in the literatures. Finally, some numerical examples and a simulation are given to show the effectiveness of the obtained result.

Input-output approach to robust stability and stabilization for uncertain singular systems with time-varying discrete and distributed delays

Based on input-output approach, the robust stability and stabilization problems for uncertain singular systems with time-varying delays are investigated. The parameter uncertainties are assumed to be norm-bounded and the time-varying delays include both discrete delay and distributed delay. By introducing a new input-output model, the time-delay system is embedded in a family of systems with a forward system without time delay and a dynamical feedback uncertainty. A sufficient and necessary condition, which guarantees the system regular, impulse-free and stable for all admissible uncertainties, is obtained. Based on the strict linear matrix inequality, the desired robust state feedback controller is also obtained. Finally, a numerical example is provided to demonstrate the application of the proposed method.

Robust stability and stabilization for uncertain discrete-time switched singular systems with time-varying delays

The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated.By constructing a novel switched Lyapunov-Krasovskii functional,a delay-dependent criterion for the unforced system to be regular,causal and uniformly asymptotically stable is established in terms of linear matrix inequalities（LMIs）.An explicit expression for the desired memoryless state feedback stabilization controller is also given.The merits of the proposed criteria lie in their less conservativeness and relative simplicity,which are achieved by considering additionally useful terms（ignored in previous methods） when estimating the upper bound of the forward difference of the Lyapunov-Krasovskii functional and by avoiding utilizing any model augmentation transformation.Some numerical examples are provided to illustrate the validity of the proposed methods.

Further Results on Delay-distribution-dependent Robust Stability Criteria for Delayed Systems

This paper concerns the robust stability analysis of uncertain systems with time delays as random variables drawn from some probability distribution. The delay-distribution-dependent criteria for the exponential stability of the original system in mean square sense are achieved by Lyapunov functional method and the linear matrix inequality （LMI） technique. The proposed approach involves neither free weighting matrices nor any model transformation, and it shows that the new criteria can provide less conservative results than some existing ones. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.

New delay-dependent robust stability and stabilization for uncertain T-S fuzzy time-delay systems under imperfect premise matching

To alleviate the conservativeness of the stability criterion for Takagi-Sugeno （T-S） fuzzy time-delay systems, a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function with an additional triple-integral term, which was firstly u3ed to derive the stability criterion for T-S fuzzy time-delay systems. By the same approach, the robust stability issue for fuzzy time-delay systems with uncertain parameters was also considered. On the other hand, in order to enhance the design flexibility, a new design approach for uncertain fuzzy time-delay systems under imperfect premise matching was also proposed, which allows the fuzzy controller to employ different membership functions from the fuzzy time-delay model. By the numerical examples, the proposed stability conditions are less conservative in the sense of getting larger allowable time-delay and obtaining smaller feedback control gains. For instance, when the allowable time-delay increases from 7.3 s to 12 s for an uncertain T-S fuzzy control system with time-delay, the norm of the feedback gains decreases from （34.299 2, 38.560 3） to （10.073 3, 11.349 0）, respectively. Meanwhile, the effectiveness of the proposed design method was illustrated by the last example with the robustly stable curves of system state under the initial condition of x（0） = [3 -1].

New Robust Exponential Stability Analysis for Uncertain Neural Networks with Time-varying Delay

In this paper,the global robust exponential stability is considered for a class of neural networks with parametric uncer- tainties and time-varying delay.By using Lyapunov functional method,and by resorting to the new technique for estimating the upper bound of the derivative of the Lyapunov functional,some less conservative exponential stability criteria are derived in terms of linear matrix inequalities (LMIs).Numerical examples are presented to show the effectiveness of the proposed method.

Stability and Robust Stability of Switched Positive Linear Systems With All Modes Unstable

This paper is concerned with the stability and robust stability of switched positive linear systems(SPLSs) whose subsystems are all unstable. By means of the mode-dependent dwell time approach and a class of discretized co-positive Lyapunov functions, some stability conditions of switched positive linear systems with all modes unstable are derived in both the continuous-time and the discrete-time cases, respectively. The copositive Lyapunov functions constructed in this paper are timevarying during the dwell time and time-invariant afterwards. In addition, the above approach is extended to the switched interval positive systems. A numerical example is proposed to illustrate our approach.

Delay-dependent criteria for the robust stability of systems with time-varying delay

The problem of delay-dependent robust stability for systems with time-varying delay has been considered. By using the S-procedure and the Park's inequality in the recent issue, a delay-dependent robust stability criterion which is less conservative than the previous results has been derived for time-delay systems with time-varying structured uncertainties. The same idea has also been easily extended to the systems with nonlinear perturbations. Numerical examples illustrated the effectiveness and the improvement of the proposed approach. Keywords Delay-dependent criteria - Robust stability - Time-varying structured uncertainties - Nonlinear perturbations - Linear matrix inequality This work was supported by the Doctor Subject Foundation of China (No. 2000053303).

Delay-dependent Criteria for Robust Stability of Uncertain Switched Hopfield Neural Networks

This paper deals with the problem of delay-dependent robust stability for a class of switched Hopfield neural networks with time-varying structured uncertainties and time-varying delay. Some Lyapunov-KrasoVskii functionals are constructed and the linear matrix inequality （LMI） approach and free weighting matrix method are employed to devise some delay-dependent stability criteria which guarantee the existence, uniqueness and global exponential stability of the equilibrium point for all admissible parametric uncertainties. By using Leibniz-Newton formula, free weighting matrices are employed to express this relationship, which implies that the new criteria are less conservative than existing ones. Some examples suggest that the proposed criteria are effective and are an improvement over previous ones.

ROBUST STABILITY ANALYSIS FOR RAILWAY VEHICLE SYSTEMS

The lateral stability for railway vehicle dynamic system with uncertainparameters and nonlinear uncertain force vector is studied by using the Lyapunov stability theory. Arobust stability condition for the considered system is derived, and the obtained stability boundsare not necessarily symmetric with respect to the origin in the parameter space. The lateralstability analysis for a railway bogie model is analyzed by using the proposed approach. Thesymmetric and asymmetric results are both given and the influence of the adjustable parameter betaon the stability bounds is also discussed. With the help of the proposed method, the robuststability analysis can provide a reference for the design of the railway vehicle systems.