Conservative Stability Analysis Research Articles

State-feedback memory control for uncertain cyber-physical systems under Denial-of-Service attacks*

This paper tackles the problem of state-feedback control for uncertain cyber-physical systems with the presence of Denial-of-Service attacks. The closed-loop stability is guaranteed through a new state-feedback packet-based strategy that utilizes past states (memory) to artificially enrich the control dynamics. The presence of an energy-bounded attacker is assumed and the closed-loop system under attack is modeled as an uncertain switched system. A less conservative stability analysis condition based on the Lyapunov theory is used as starting point for the synthesis conditions, which are formulated in terms of Linear Matrix Inequalities. Numerical experiments are conducted to illustrate the technique's effectiveness and perform comparisons with packet-based methods from the literature.

Delay-Variation-Dependent Criteria on Stability and Stabilization for Discrete-Time T–S Fuzzy Systems With Time-Varying Delays

This article is concerned with the stability and stabilization of delayed discrete-time T–S fuzzy systems. The purpose is to develop less conservative stability analysis and state-feedback controller design methods. First, a matrix-separation-based inequality is proposed, which can provide a tighter estimation for the augmented summation term. Then, by constructing a delay-product-type Lyapunov–Krasovskii functional, using the proposed inequality to estimate its forward difference and using a cubic functional negative-determination lemma to handle nonconvex conditions with respect to the delay, a delay and its variation-dependent stability criterion are obtained. Moreover, the corresponding controller design method for closed-loop delayed fuzzy systems is derived via parallel distributed compensation scheme. Finally, two examples are given to demonstrate the effectiveness and merits of the proposed approaches.

Seismic internal stability of bilinear geosynthetic-reinforced slopes with cohesive backfills

The bilinear geosynthetic-reinforced slope (BGRS) is a new two-tier reinforced earth structure without an offset. Analyzing its seismic internal stability is aimed to determine the resultant reinforcement force. In this paper, using a top-down log spiral mechanism, the moment limit equilibrium equations are established to formulate the resultant reinforcement forces for upper and lower tiers of the BGRS, considering influence of angle of lower tier, depth of tension crack, cohesion of backfill and pseudo-static seismic loads. Results show that ignoring cohesion of backfill and/or vertical upward seismic load is beneficial to conservative stability analysis, and the existence of tension cracks changes the distribution of reinforcement forces in upper and lower tiers. Additionally, the critical slip surface is also studied, which is found that the volume of the failure body decreases under the global stability with increase of angle of lower tier, cohesion of backfill or depth of tension crack, or with the decrease of seismic coefficients.

A Novel Method for Guaranteed Overflow Oscillation Elimination in Digital Filters Subject to Quantization

This brief provides a novel criterion for the analysis of convergence of states of an infinite impulse response (IIR) digital filter to a bounded region under the influence of composite effects of quantization and overflow nonlinearities. The developed criterion is less conservative in its approach in terms of analyzing stability than conventional methods and can be employed for implementation of an IIR filter on comparatively smaller hardware word-length than existing methods. The conventional approaches consider asymptotic stability of a filter with respect to the quantization noise; however, quantization in digital filters can result into bounded oscillation and lead to infeasibility of the asymptotic stability. Therefore, a less conservative stability analysis together with estimation of steady-state region of convergence for an IIR filter is provided. In addition, the conventional approaches, analyzing stability, and steady-state region of convergence, may not guarantee an overflow oscillation-free realization of a filter. Consequently, a condition for estimating the steady-state region of convergence (along with the filter stability) with an additional constraint that the filter’s state should not overflow in the bounded region has been derived. A comparative analysis with conventional methods is provided in simulation results.

Delay-dependent robust absolute stability of uncertain Lurie singular systems with neutral type and time-varying delays

This paper is concerned with the robust absolute stability analysis for Lurie control of the neutral singular systems. By using Lyapunov–Krasovskii function method, delay dependent criteria for absolute stability of system are derived in terms of Linear Matrix Inequality. The difference between this paper and other existing results is that the lower bounds and upper bounds of discrete-delay are considered, which will obtain some less conservative stability analysis results. Finally, some numerical examples are presented to illustrate the effectiveness of the method.

New delay‐dependent exponential stability for neutral Markovian jump systems with mixed delays and nonlinear perturbations

SummaryThis paper deals with the problem of delay‐dependent exponential stability for neutral Markovian jump systems with mixed delays and nonlinear perturbations. Based on Lyapunov stability theory and linear matrix inequality method, some new exponential stability criteria are presented. The difference between this paper and other existing results is that the lower bounds of the neutral delay, the upper bounds of the neutral delay and discrete delay are considered, which will obtain some less conservative stability analysis results. Numerical examples are given to show that the proposed criteria improve the existing results.

A study on the effect of utilizing different constitutive models in the stability analysis of an underground gas storage within a salt structure

Constructing caverns by the use of solution mining in salt structures creates reservoirs with large dimensions and low working costs. Additionally, the special properties of rock salt have caused salt structures recognized, for decades in industrial countries, as one of the best geo formations for storage of energy resources—including oil, natural gas, compressed air and nuclear waste. Storage of natural gas as the second most in-demand fuel gives it a special importance. In fact countries’ ability to store natural gas has played an important role in their energy managements.Predicting the behavior of gas storage reservoirs, constructed in salt structure, is extraordinarily important. By making such predictions, likely problems in operation time, such as instability and convergence, can be prevented. It can also be used to estimate maximum and minimum allowable gas pressure, one of the most important operational parameters.Until now, researchers have used different constitutive models to predict the behavior of underground gas storage. The most common among these, are the Burger analytic model, Power Law, and WIPP1 empirical models. By utilizing these three models in this research, the results show that the Power Law and WIPP models are more capable of predicting storage reservoir behavior; also that the Power Law model offers a more conservative stability analysis.

Stability Analysis of Polynomial-Fuzzy-Model-Based Control Systems With Mismatched Premise Membership Functions

This paper investigates the stability of polynomial-fuzzy-model-based (PFMB) control system, which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop. To enhance the design flexibility, the number of rules and the shape of premise membership functions of the polynomial fuzzy controller are considered to be chosen freely and are different from those of the polynomial fuzzy model, however, which make the stability analysis more difficult and potentially lead to conservative stability analysis result. A sum-of-squares (SOS)-based stability analysis approach using the Lyapunov stability theory is proposed to investigate the stability of the PFMB control systems and synthesize the polynomial fuzzy controller. To facilitate the stability analysis and relax the stability analysis result, the property of the membership functions and the boundary information of the membership grades and premise variables are taken into account in the stability analysis and incorporated into the SOS-based stability conditions. A simulation example is given to illustrate the effectiveness of the proposed approach.

New delay-dependent robust stability criteria for uncertain neutral systems with mixed delays

This paper investigates the problem of robust stability for neutral type system with mixed delays and time-varying structured uncertainties. Based on Lyapunov stability theory and linear matrix inequalities (LMIs) method, some new stability criteria are presented. The difference between this paper and other existing results is that the lower bounds and upper bounds of the neutral-delay and discrete-delay are considered, which will obtain some less conservative stability analysis results. Several numerical examples are given to demonstrate the effectiveness and merit of the proposed results.

On delay-dependent stability conditions for Takagi–Sugeno fuzzy systems

This paper presents new less conservative stability analysis conditions for Takagi–Sugeno fuzzy systems subject to interval time-varying delay. The methodology is based on the direct Lyapunov method allied with an appropriate Lyapunov–Krasovskii functional choice and the use of the integral inequalities, Finsler lemma, Newton–Leibniz formula manipulations and convex combination properties. Particularly, the main result differs from previous ones since the positiveness of the Lyapunov–Krasovskii functional is guaranteed by new relaxed conditions. Two examples illustrate the effectiveness of the proposed methodology.

Stability Analysis and Stabilization of T-S Fuzzy Delta Operator Systems with Time-Varying Delay via an Input-Output Approach

The stability analysis and stabilization of Takagi-Sugeno (T-S) fuzzy delta operator systems with time-varying delay are investigated via an input-output approach. A model transformation method is employed to approximate the time-varying delay. The original system is transformed into a feedback interconnection form which has a forward subsystem with constant delays and a feedback one with uncertainties. By applying the scaled small gain (SSG) theorem to deal with this new system, and based on a Lyapunov Krasovskii functional (LKF) in delta operator domain, less conservative stability analysis and stabilization conditions are obtained. Numerical examples are provided to illustrate the advantages of the proposed method.

Soliton-plasmon resonances as Maxwell nonlinear bound states

We demonstrate that soliplasmons (soliton-plasmon bound states) appear naturally as eigenmodes of nonlinear Maxwell's equations for a metal/Kerr interface. Conservative stability analysis is performed by means of finite element numerical modeling of the time-independent nonlinear Maxwell equations. Dynamical features are in agreement with the presented nonlinear oscillator model.

Improved synthesis method for network-based control

A less conservative stability analysis condition for closed-loop delayed linear systems subjected to uncertain, bounded, non-differentiable, additive time delays is presented. The obtained stability condition is applied to the problem of networked control system robust design in the presence of network-induced delays and data packet dropouts. Illustrative examples are provided to show the advantage and applicability of the developed results in this case.

Sampled-data fuzzy-model-based control systems: stability analysis with consideration of analogue-to-digital converter and digital-to-analogue converter

This study investigates the system stability of sampled-data fuzzy-model-based control systems. To conduct the stability analysis, Takagi-Sugeno (T-S) fuzzy model is employed to represent the continuous-time non-linear plant. Based on the fuzzy model, a sampled-data fuzzy controller is proposed to perform the control task. By using a digital computer or microcomputer, the sampled-data fuzzy controller can be realised at low implementation cost. However, the following difficulties are needed to be addressed to put the sampled-data fuzzy controller into practice. First, as the zero-order-hold unit keeps the system states and control signal constant during the sampling period, the immediate system states cannot be accessed to compute the required control signal as what the continuous-time fuzzy control does. Second, the analogue-to-digital and digital-to-analogue converters introduce quantisation error to the control process, which is a source of instability. Third, the sampling activity introduces discontinuity to complicate the system dynamics, which makes the stability analysis difficult. Furthermore, it is due to the sampling activity and zero-order-hold unit, the nice property of continuous-time fuzzy-model-based control system for stability analysis vanishes which leads to conservative stability analysis results. In this study, these difficulties are addressed and the system stability is investigated based on the Lyapunov stability theorem. Membership function conditions are developed to facilitate the stability analysis. An application example is presented to illustrate the effectiveness of the proposed approach.

Stability and stabilization of aperiodic sampled-data control systems using robust linear matrix inequalities

Stability analysis of an aperiodic sampled-data control system is considered for application to networked and embedded control. The stability condition is described in a linear matrix inequality to be satisfied for all possible sampling intervals. Although this condition is numerically intractable, a tractable sufficient condition can be constructed with the mean value theorem. Special attention is paid to tightness of the sufficient condition for less conservative stability analysis. A region-dividing technique for the reduction of conservatism and generalization to stabilization are also discussed. An example demonstrates the efficacy of the approach.