Robust Stability Criteria Research Articles

New Robust Stability Criteria for Lur’e Systems with Time-varying Delays and Sector-bounded Nonlinearities

This paper deals with a robust stability problem for uncertain Lur’e systems with time-varying delays and sector-bounded nonlinearities. An improved delay-dependent robust stability criterion is proposed via a modified Lyapunov-Krasovskii functional (LKF) approach. Firstly, a modified LKF consisting of delay-dependent matrices and double-integral items under two delay subintervals is constructed, thereby making full use of the delay and its derivative information. Secondly, the stability criteria can be expressed as convex linear matrix inequality (LMI) via the properties of quadratic function application. Thirdly, to further reduce the conservatism of stability criteria, the quadratic generalized free-weighting matrix inequality (QGFMI) is used. Finally, some numerical examples, including the Lur’e system and the general linear time-delayed system, are presented to show the improvement of the proposed approach.

Robust stability analysis of interval fractional-order plants by fractional-order controllers: an approach to reduce additional calculation

This paper investigates the robust stability of fractional-order plants suffering from interval uncertainties by using fractional-order controllers. Based on the zero-exclusion principle, at first, new necessary and sufficient criteria are proposed to analyze the robust stability of the corresponding characteristic polynomial. Then, an auxiliary function is presented to investigate the robust stability criteria. The results of this paper also help to reduce additional calculations noticeably since the vertices used in the auxiliary function are fixed for all positive frequencies. Finally, three numerical examples are given to indicate the effectiveness of the paper results.

Robust stability analysis for feedback systems with simultaneous uncertainties via IQCs

The robust stability of feedback interconnections is studied for a class of continuous-time causal linear systems over finite-energy signals of non-uniformly lower-bounded support. The stability of the feedback system with simultaneous uncertainties in the plant and the controller is exploited via integral quadratic constraints (IQCs), in which the plants and controllers are taken from two path-connected uncertainty sets with respect to the Feintuch's time-varying gap metric. Subsequently, the robust stability of the two-port networked system is characterised by means of the combination of IQCs and the time-varying gap. In particular, some robust stability criteria are applicable to the linear systems that do not have strong graph representations.

Receptance-based robust stability criteria for second-order linear systems with time-varying delay and unstructured uncertainties

This paper presents new frequency domain criteria for the robust stability analysis of closed-loop second-order systems under time-varying internal delay. The proposed approach is derived from the small gain theorem for systems described by the versatile system receptance to guarantee robust stability despite time-varying delays and model uncertainties. Robust stability of systems with time-varying delays is challenging to cope because time-invariant paradigm does not hold, but the proposed approach is directly based on the frequency response analysis of the closed-loop system with unstructured uncertainty bound. The criteria can be applied to either single or multiple inputs systems, and no constraint is imposed on the delay derivative. A simple receptance-based Internal Model Control strategy is proposed to improve robust stability margins while nominal state-feedback design is preserved. Thus, a controller obtained from the delay-free nominal model can be used to ensure the robust stability of the uncertain second-order system with time-varying delay. Simulation case studies are used to illustrate the benefits of the proposed criteria.

Robust stochastic stability for multi-group coupled models with Markovian switching

As one of the most important topics in control theory, robust stability for the systems plays a key role in many areas of science and industry. This paper discusses the robust stochastic stability a class of multi-group coupled stochastic models with Markovian switching. Based on discrete-time observations in the diffusion part with time-delay, the robust stochastic exponential stability criterion in mean square sense is established in the forms of Lyapunov-type and coefficient-type. An application to the robust stochastic stability for a class of coupled oscillators is proposed.

Stability and Stabilization of T–S Fuzzy Time-Delay System via Relaxed Integral Inequality and Dynamic Delay Partition

This article investigates delay-dependent stability analysis and stabilization for continuous Takagi–Sugeno fuzzy systems with a time-varying delay. By employing dynamic delay partition, the delay interval <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$[0, d(t)]$</tex-math></inline-formula> is partitioned into some variable subintervals so that much more information of time-varying delay can be utilized. Moreover, a novel relaxed integral inequality is applied to estimate the derivative of Lyapunov–Krasovskii functionals for achieving reduction of estimation gap. As a result, several further robust stability and stabilization criteria with less conservativeness are proposed. Finally, three examples are provided to demonstrate the effectiveness and advantages of the presented methods.

Contribution of GCSC to regulate the frequency in multi-area power systems considering time delays: A new control outline based on fractional order controllers

This paper addresses the application of the gate controlled series capacitor (GCSC) in coordination with automatic generation control (AGC) for providing better dynamic responses in interconnected multi-area power systems. A novel controller scheme called Hybrid controller for modeling the GCSC is proposed. The proposed control model consists of a fractional-order proportional-integral-derivative (FOPID) controller and a tilt-integral-derivative (TID) one. Optimized coefficients of the controllers are obtained by applying the Sine-Cosine algorithm (SCA). The delay in communication links as a common feature in wide area control of power systems may cause instability problem. So, a robust stability criterion is presented to estimate the maximum delay time which allows an AGC scheme embedded with the GCSC damping controller to retain stable. Comprehensive discussions are presented on a deregulated two-area power system and a traditional three-area one. Simulation results confirm that the proposed Hybrid controller is capable to achieve better dynamic responses and provide better coordination between the GCSC and AGC in comparison to the other coordinated controllers including PID-based GCSC-AGC, TID-based GCSC-AGC, and FOPID-based GCSC-AGC ones. Eventually, the sensitivity analysis is accomplished to assess the robustness property of the proposed controller against the variations of the parameters.

New Robust Stability Criteria for Uncertain Neutral Time-Delay Systems With Discrete and Distributed Delays

New Robust Stability Criteria for Uncertain Neutral Time-Delay Systems With Discrete and Distributed Delays

Robust stability criterion for perturbed singular systems of linearized differential equations

In this article, we consider a class of singular linear systems of differential equations whose coefficients are constant matrices, and study the response of its stability after a perturbation is applied into the system. We use a linear fractional transformation and through its properties we provide a practical test for robust stability. This test requires only the knowledge of the invariants of the initial system. This means it can be used without resorting to any further processes of computations to obtain invariants of any other perturbed system. Finally, numerical examples are given to support and discuss practical applications of the proposed theory.

High-Order Polynomial Observer Design for Robust Adaptive Synchronization of Uncertain Fractional-Order Chaotic Systems

Our focus in this paper is to present a new procedure of designing a high-order robust observer for chaos synchronization of a general class of uncertain nonlinear system with fractional-order derivative, using an adaptive strategy together with some parameter adjusting mechanisms. Some less stringent conditions for the exponential and asymptotic stability of adaptive robust control systems with fractional order are derived. A criterion for robust stability of an error system is obtained using the master–slave synchronization concept together with the Lyapunov stability theory associated with some algebraic manipulations. The high polynomial observer which can guarantee the robust stability of the closed loop system also rejects the effect of perturbations on the system dynamics within a prescribed level. The findings of this research are illustrated using computer simulations for the control problem of fractional Genesio–Tesi system. The proposed approach offers a systematic design procedure of a robust polynomial observer for the chaos synchronization of a large class of nonlinear systems.

Robust mean square stability of delayed stochastic generalized uncertain impulsive reaction-diffusion neural networks

This article is dedicated to the investigation of the stability problem of delayed stochastic generalized uncertain impulsive reaction-diffusion neural networks (SGUIRDNNs). Applying Lyapunov second method, several new robust mean square stability criteria on the equilibrium point of the delayed SGUIRDNNs are derived in terms of linear matrix inequalities (LMIs). At last, we provide a numerical example to verify the validity of our findings.

Dual-terminal event triggered control for cyber-physical systems under false data injection attacks

This paper deals with the problem of security-based dynamic output feedback control of cyber-physical systems (CPSs) with the dual-terminal event triggered mechanisms (DT-ETM) under false data injection (FDI) attacks. Considering the limited attack energy, FDI attacks taking place in transmission channels are modeled as extra bounded disturbances for the resulting closed-loop system, thus enabling $H_{\infty}$ performance analysis with a suitable $\varrho$ attenuation level. Then two buffers at the controller and actuator sides are skillfully introduced to cope with the different transmission delays in such a way to facilitate the subsequent security analysis. Next, a dynamic output feedback security control (DOFSC) model based on the DT-ETM schemes under FDI attacks is well constructed. Furthermore, novel criteria for stability analysis and robust stabilization are carefully derived by exploiting Lyapunov-Krasovskii theory and LMIs technique. Finally, an illustrative example is provided to show the effectiveness of the proposed method.

On robust stability of incommensurate fractional-order systems

This paper investigates the robust stability of fractional-order systems described in pseudo-state space model with incommensurate fractional orders. An existing non-conservative robust stability criterion for integer-order systems is extended to incommensurate-order fractional systems by using the generalized Nyquist Theorem. Some robust stability conditions for various uncertainty structures are proposed by employing the proposed criterion. Moreover, we focus on the interval uncertainty structure to discuss the conservatism of the common methods. A numerical example is provided to investigate that how the fractional-order of each pseudo-state can affect the robustness of the system. The effectiveness of the proposed methods is compared by applying them on the problem of space tether deployment with fractional-order control law.

Stability Analysis and Robust H∞ Controller Synthesis with Derivatives of Membership Functions for T-S Fuzzy Systems with Time-varying Delay: Input-output Stability Approach

This paper investigates the problem of delay dependent stability and H∞ control design with derivatives of membership functions of uncertain Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. A model transformation is employed by considering a three-term approximation of delayed state vector. Using Scaled Small Gain (SSG) theorem and fuzzy weighting-dependent Lyapunov functions with some useful slack variables, less conservative robust stability and stabilization criteria are formulated in terms of linear matrix inequalities (LMIs), which can be easily solved by using standard numerical packages. Finally, numerical experiments are presented to illustrate the effectiveness of the proposed method.

Adaptive Event-Triggered Load Frequency Control of Multi-Area Power Systems Under Networked Environment via Sliding Mode Control

The robust stability and stabilization of adaptive event-triggered load frequency control (LFC) with sliding mode control (SMC) for multi-area power systems under a networked environment are investigated in this paper. The adaptive event-triggered scheme is proposed to maximize network bandwidth utilization, and it can be adaptively modified according to circumstances. Furthermore, to provide stronger robustness performance which is against the frequency deviation induced by power unbalance or transmission time delays, the SMC is developed. Then, the LFC scheme for multi-area power systems under the networked environment is modeled as a Markov jump linear system model, to describe the uncertainty parameters and external disturbances better in this system. Additionally, by employing Wirtinger-based inequality and Lyapunov theory, the robust stability and stabilization criteria with less conservatism are derived. Finally, simulations are performed to demonstrate the efficacy and superiority of the developed approach.

Parametric analysis for optimized piezoelectric bistable vibration energy harvesters

This study focuses on vibration energy harvesting with piezoelectric bistable inertial generators in order to provide an alternative or a support to chemical batteries in the power supply of isolated wireless sensors (leading to a better autonomy of these devices). The objective of the present work is to provide guidelines to optimize this kind of generator through the investigation of the influence of different parameters (load resistance, mass, stiffness, buckling level) on its frequency response. These guidelines will be obtained exploiting a new analytical model for piezoelectric bistable harvesters which will be constructed based on a recent model introduced for electromagnetic bistable harvesters. This model includes the study of subharmonic behaviors which can be used to enhance the global bandwidth of the harvester as well as a stability robustness criterion which allows a better prediction of experimental observations. The new model will be validated by experimental data and finally exploited to provide guidelines for piezoelectric bistable harvester optimization.

Stability and control of uncertain ICPT system considering time‐varying delay and stochastic disturbance

SummaryThis paper studies the problem of robust exponential stability for uncertain inductively coupled power transfer (ICPT) system considering time‐varying delay and stochastic disturbance. Firstly, the model of the system is set up via a time domain method. Secondly, based on the Newton‐Leibnitz formula and stability theory, a new stability analysis of the ICPT system with uncertain parameter and time‐varying delay or stochastic disturbance is presented respectively. The proposed approach can be applied for analyzing other similar systems, and the obtained results can be also used for estimating convergence rate and region of stability. Thirdly, based on the Lyapunov‐Krasovskii functional (LKF) approach and the stochastic stability theory, robust exponential stability criteria in the mean square are derived and the relevant controller is designed. The proposed method can further reduce conservatism. Finally, the correctness and effectiveness of the obtained results are verified by an example and simulations indicate that the larger time delay, the slower attenuation. Simultaneously, the uncertain parameter and the stochastic disturbance have a significant influence on the region of stability. In addition, in respect of reducing conservatism, the effectiveness of the proposed method is demonstrated by comparing with other papers. In addition, the designed controller shows better performance for the ICPT system with the parameter uncertainty, the time‐varying delay, and the stochastic disturbance.

New delay-dependent robust exponential stability for uncertain linear systems with multiple non-differentiable time-varying delays and nonlinear perturbations

This paper studies delay-dependent robust stability analysis for uncertain linear systems with constant delay, time-varying delay and nonlinear perturbations. The restriction on the derivative of time-varying delay is removed, which means that the fast time-varying delays are allowed. Combined with Leibniz-Newton formula, integral inequalities, Wirtinger-based integral inequality, Peng-Park’s integral inequality, utilization of zero equation and new Lyapunov-Krasovskii functional have been adopted to study. New delay-dependent robust stability criteria for uncertain time-delay systems are established in terms of linear matrix inequalities (LMIs). Numerical examples and simulation suggest that the results given to illustrate the effectiveness and improvement over some existing methods.

Robust Scale-Free Synthesis for Frequency Control in Power Systems

The ac frequency in electrical power systems is conventionally regulated by synchronous machines. The gradual replacement of these machines by asynchronous renewable-based generation, which provides little or no frequency control, increases system uncertainty and the risk of instability. This imposes hard limits on the proportion of renewables that can be integrated into the system. In this paper, we address this issue by developing a framework for performing frequency control in power systems with arbitrary mixes of conventional and renewable generation. Our approach is based on a robust stability criterion that can be used to guarantee the stability of a full power system model on the basis of a set of decentralized tests, one for each component in the system. It can be applied even when using detailed heterogeneous component models, and can be verified using several standard frequency response, state-space, and circuit theoretic analysis tools. Furthermore, the stability guarantees hold independently of the operating point, and remain valid even as components are added to and removed from the grid. By designing decentralized controllers for individual components to meet these decentralized tests, every component can contribute to the regulation of the system frequency in a simple and provable manner. Notably, our framework certifies the stability of several existing (nonpassive) power system control schemes and models, and allows for the study of robustness with respect to delays.

Stability analysis and output-feedback synthesis of hybrid systems affected by piecewise constant parameters via dynamic resetting scalings

We develop novel criteria for robust stability of a class of hybrid systems that are affected by piecewise constant uncertain parameters with dwell-time constraints. These criteria result from clock-dependent Lyapunov arguments that are based on several new robust stability conditions for continuous-time linear time-invariant systems which are affected by parametric passive uncertainties and do not admit any discrete dynamics. In contrast to other approaches, our stability analysis results rely on separation techniques from robust control involving dynamic resetting scalings. Moreover, these techniques are expected to pave the way for covering much more general uncertainties within the framework of integral quadratic constraints. Building upon the new insights on robust stability, we are able to propose an output-feedback gain-scheduling design methodology similarly to our recently obtained synthesis result involving dynamic resetting D-scalings. Most of the obtained conditions are expressed as infinite-dimensional (differential) linear matrix inequalities which can be numerically solved by using relaxation methods based on, e.g., linear splines or matrix sum-of-squares. We apply our results to obtain novel stability criteria and to design distributed controllers for networked systems over undirected switching topologies. Finally, the approach is illustrated with several numerical examples.