Piecewise Lyapunov-Krasovskii Functionals Research Articles

Output feedback pinning control for complex dynamical networks subjected to multiple attacks

This paper is concentrated on the secure synchronization control issue for complex dynamical networks (CDNs) subjected to multiple attacks. For the sake of conserving resources and being closer to reality, a new output feedback controller based on pinning nodes is firstly designed. Secondly, in contrast with the existent researches on secure network circumstances, we establish a novel multiple attacks model considering the influence of random deception attacks and aperiodic Denial-of-Service (DoS) attacks. Based on the piecewise Lyapunov-Krasovskii function and decoupling method, a new secure synchronization criterion is proposed to realize the mixed H∞ and passive performance of CDNs against multiple attacks, and the control gain is gained. Lastly, the availability of the raised consequence is testified by two concrete examples.

Consensus Control of Multiagent Systems Under Switching Topology and Denial-of-Service Attacks

This article studies the consensus problem of multiagent systems (MASs) under denial-of-service (DoS) attacks and switching topology. Compared with the previous papers, under the switching topology, the impact of DoS attacks on the MAS is considered, and thus, the difficulty of consensus protocol design is further increased. First, a piecewise resilient consensus protocol is proposed to ensure that the MAS can achieve consensus under switching topology and DoS attacks. Then, by considering the different convergence rates caused by the switching topology in each sleep period of DoS attacks, a piecewise Lyapunov–Krasovskii function is established. The sufficient conditions on the global convergence of the system are obtained under switching topology and DoS attacks. In the meantime, the lower bound of average dwell time of the switching topology is determined under DoS attacks. The relationship between average dwell time and the parameters of DoS attacks is discussed. Finally, the simulation example is conducted to verify the effectiveness of the proposed method.

Observer-based defense control for networked Takagi-Sugeno fuzzy systems against asynchronous DoS attacks

This article investigates the defense control problem for sampled-data Takagi-Sugeno (T-S) fuzzy systems with multiple transmission channels against asynchronous denial-of-service (DoS) attacks. Firstly, a new switching security control method is proposed to tolerate the asynchronous DoS attacks that act independently on each channel. Then, based on switching strategy, the resulting augmented sampled-data system can be converted into new switched systems including several stable subsystems and one open-loop subsystem. Besides, by applying the piecewise Lyapunov-Krasovskii (L-K) function method, membership functions (MFs) dependent sufficient conditions are derived to ensure the exponential stability of newly constructed switching systems. Moreover, quantitative relations among the sampling period, the exponential decay rate, and the rate of all channels being fully attacked and not being completely attacked are established. Finally, simulation examples show the effectiveness of the developed defense control approach.

Asynchronous $$H_{\infty }$$ Control of Uncertain Switched Singular Systems with Time-Varying Delays

This paper is concerned with the problem of $$H_{\infty }$$ control for a class of uncertain switched singular systems with time-varying state delays under asynchronous switching. The asynchronous phenomenon is caused by the choice of controller lagging behind the corresponding subsystem in practice. First, sufficient conditions by finding a novel piecewise Lyapunov–Krasovskii function combining with average dwell time technique are given to guarantee the exponential admissibility of the system. The algebraic equations and differential equations of the original system are proved to be exponentially stable. Then, a condition guaranteeing the $$H_{\infty }$$ performance of the original system is derived based on the above analysis. Furthermore, strict LMI formulas for solving the state feedback controller are given. Finally, the effectiveness of the proposed methods is illustrated by numerical examples.

Fault Detection and Controller Co-Design for Nonlinear Delayed Switched Systems Based on Mode-Dependent Average Dwell Time Under Asynchronous Switching

In this paper, the fault detection (FD) and controller co-design problem is investigated for continuous-time nonlinear delayed switched systems based on mode-dependent average dwell time (MDADT) under asynchronous switching. Different from the average dwell time (ADT) method, the adopted MDADT switching law in which each subsystem has its own ADT, is more suitable for practical applications. Meanwhile, a closed-loop control strategy including both the controller and the fault detection filter, are designed simultaneously by using piecewise Lyapunov-Krasovskii function (LKF), MDADT method and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H_\infty }$ </tex-math></inline-formula> control technique. Furthermore, both the Wirtinger integral inequality and an advanced reciprocal convex combination method are utilized to provide a tighter estimation on continuous derivative of certain LKF, leading to a less conservative result, and the solution of the parameters for the controller and fault detection filter (FDF) is characterized in the feasibility of LMI problem. Finally, a practical designed solution on the highly maneuverable aircraft technology indicates the proposed technique is valid and superior.

Event-triggered attack-tolerant tracking control design for networked nonlinear control systems under DoS jamming attacks

This paper addresses the problem of event-triggered attack-tolerant tracking control for a networked nonlinear system under spasmodic denial-of-service (DoS) attacks. Compared with some existing results, theexact duration of DoS attacks is not required while only assuming attainable bounds of attack frequency and duration. First, a new event-triggered attack-tolerant fuzzy tracking controller is proposed, to reduce the amount of sensor data transmissions over the sensor-to-controller (S-C) channel while counteracting unknown DoS attacks. Second, for the purpose of performance analysis and synthesis, a unified event-triggered Takagi-Sugeno (T-S) fuzzy switched model is established, which accounts for a suitable attack-resilient event-triggered communication scheme and unknown DoS jamming signals.Third, using piecewise Lyapunov-Krasovskii functional (PLKF) analysis technique, a newcriterion is derived to ensure exponential stability of the resulting switched tracking error system while achieving a weighted $H_{\infty}$ performance level. Additionally, the relationship among the parameters of a DoS attack signal, thetriggering parameters, the fuzzy controller gains, the sampling period, andthe decay rate can be quantitatively characterized. Moreover, the triggering matrix parameter and fuzzy controller gains are obtained by finding a feasible solution to a set of linear matrix inequalities (LMIs).Finally, numerical verification is performed to demonstrate the effectiveness of the proposed control design method.

Asynchronous Event-Triggered Control for Networked Interval Type-2 Fuzzy Systems Against DoS Attacks

This article investigates the asynchronous adaptive event-triggered control problem for networked interval type-2 (IT2) fuzzy systems subject to nonperiodic denial-of-service (DoS) attacks. Unlike some existing results, two resilient adaptive event-triggered mechanisms (AETMs) are applied independently to both sensor and controller output while resisting nonperiodic DoS attacks. In particular, the asynchronous resilient AETM thresholds are adaptively varied based on error information between current sampling and latest available packets. Then, a new switched IT2 fuzzy dynamical output feedback system is modeled by discussing the influence of the AETM and nonperiodic DoS attacks simultaneously. Furthermore, mismatched membership functions are considered between dynamic output feedback controller and IT2 fuzzy model, and a slack matrix is introduced to relax stability conditions. Besides, by utilizing the piecewise Lyapunov-Krasovskii function method, sufficient conditions are derived to guarantee that the newly constructed switching system is globally exponentially stable with H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. Finally, the effectiveness of the developed control approach is illustrated by two examples.

Event-triggered state estimation for T-S fuzzy affine systems based on piecewise Lyapunov-Krasovskii functionals

This paper investigates the problem of event-triggered H∞ state estimation for Takagi-Sugeno (T-S) fuzzy affine systems. The objective is to design an event-triggered scheme and an observer such that the resulting estimation error system is asymptotically stable with a prescribed H∞ performance and at the same time unnecessary output measurement transmission can be reduced. First, an event-triggered scheme is proposed to determine whether the sampled measurements should be transmitted or not. The output measurements, which trigger the condition, are supposed to suffer a network-induced time-varying and bounded delay before arriving at the observer. Then, by adopting the input delay method, the estimation error system can be reformulated as a piecewise delay system. Based on the piecewise Lyapunov-Krasovskii functional and the Finsler’s lemma, the event-triggered H∞ observer design method is developed. Moreover, an algorithm is proposed to co-design the observer gains and the eventtriggering parameters to guarantee that the estimation error system is asymptotically stable with a given disturbance attenuation level and the signal transmission rate is reduced as much as possible. Simulation studies are given to show the effectiveness of the proposed method.

Stability of discrete-time systems with time-varying delay based on switching technique

In this paper, the stability problem of discrete-time systems with time-varying delay is considered. Some new stability criteria are derived by using a switching technique. Compared with the Lyapunov–Krasovskii functional (LKF) approach, the method used in this paper has two features. First, a switched model, which is equivalent to the original system and contains more delay information, is introduced. It means that the criteria obtained by using the LKF method can be regarded as stability criteria for the switched system under arbitrary switching. Second, when the switching signal is known, the stability problem for the switched model under constrained switching is considered and piecewise LKFs are adopted to obtain stability criteria. Since constrained switching is less conservative than arbitrary switching if the switching signal is known, one can know that the obtained results in this paper are less conservative than some existing ones. Two examples are given to illustrate the effectiveness of the obtained results.

L2-gain analysis for systems with interval time-varying delay based on the switching technique

In this paper, an improved scheme is proposed to solve the L2-gain analysis problem of systems with interval time-varying delay. In order to reduce the conservativeness, the considered delay system is modeled as a switched system. Then, the piecewise Lyapunov–Krasovskii functional (PLKF) method, which is more effective than the Lyapunov–Krasovskii functional (LKF) method, is adopted to obtain the L2-gain criterion. Finally, numerical examples are given to suggest the effectiveness of the proposed method.

Dwell time-based stabilisation of switched delay systems using free-weighting matrices

ABSTRACTIn this paper, we present a quasi-convex optimisation method to minimise an upper bound of the dwell time for stability of switched delay systems. Piecewise Lyapunov–Krasovskii functionals are introduced and the upper bound for the derivative of Lyapunov functionals is estimated by free-weighting matrices method to investigate non-switching stability of each candidate subsystems. Then, a sufficient condition for the dwell time is derived to guarantee the asymptotic stability of the switched delay system. Once these conditions are represented by a set of linear matrix inequalities , dwell time optimisation problem can be formulated as a standard quasi-convex optimisation problem. Numerical examples are given to illustrate the improvements over previously obtained dwell time bounds. Using the results obtained in the stability case, we present a nonlinear minimisation algorithm to synthesise the dwell time minimiser controllers. The algorithm solves the problem with successive linearisation of nonlinear conditions.

Stability and stabilization of discrete T-S fuzzy time-delay system based on maximal overlapped-rules group

The problems of stability and stabilization for the discrete Takagi-Sugeno (T S) fuzzy time-delay system are investigated. By constructing a discrete piecewise Lyapunov-Krasovskii function (PLKF) in each maximal overlapped-rules group (MORG), a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved. Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme, and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed. The above two sufficient conditions only require finding common matrices in each MORG. Compared with the common Lyapunov-Krasovskii function (CLKF) approach and the fuzzy Lyapunov-Krasovskii function (FLKF) approach, these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved. Finally, simulation examples show that the proposed PLKF approach is effective.

Decentralized piecewise [formula omitted] fuzzy filtering design for discrete-time large-scale nonlinear systems with time-varying delay

This paper investigates the problem of decentralized piecewise H∞ filtering design for a class of discrete-time large-scale nonlinear systems with time-varying delay. The considered large-scale system consists of a number of nonlinear subsystems, and each nonlinear subsystem is represented by a Takagi–Sugeno (T–S) model. The time-varying state delay of each subsystem is assumed to be of an interval-like type with lower and upper bounds. The objective is to design a decentralized piecewise filter such that the filtering error system is asymptotically stable with a guaranteed H∞ disturbance attenuation level. A two-term approximation method is proposed to transform the filtering error system into an interconnected formulation, and the decentralized H∞ filtering problem is reformulated in the context of input–output (IO) stability. Based on a piecewise Lyapunov–Krasovskii functional (PLKF) combined with the scaled small gain (SSG) theorem, less conservative results are presented for the decentralized piecewise H∞ filtering design of the large-scale T–S fuzzy system in terms of linear matrix inequalities. Two examples are provided to illustrate the effectiveness of the proposed method.

Adaptive feedback synchronisation of complex dynamical network with discrete-time communications and delayed nodes

This paper considered the synchronisation of continuous complex dynamical networks with discrete-time communications and delayed nodes. The nodes in the dynamical networks act in the continuous manner, while the communications between nodes are discrete-time; that is, they communicate with others only at discrete time instants. The communication intervals in communication period can be uncertain and variable. By using a piecewise Lyapunov–Krasovskii function to govern the characteristics of the discrete communication instants, we investigate the adaptive feedback synchronisation and a criterion is derived to guarantee the existence of the desired controllers. The globally exponential synchronisation can be achieved by the controllers under the updating laws. Finally, two numerical examples including globally coupled network and nearest-neighbour coupled networks are presented to demonstrate the validity and effectiveness of the proposed control scheme.

Exponential stability of linear distributed parameter switched systems with time-delay

In this paper, the exponential stability analysis for ODE switched systems with time delay is extended to distributed parameter switched systems (DPSS) in Hilbert space. For a given family of exponential stable subsystems, this paper focuses on finding conditions to guarantee the overall DPSS’ exponential stability. Based on semigroup theory, by applying piecewise Lyapunov-Krasovskii functionals method incorporated average dwell time approach, sufficient conditions for exponential stability are derived. These conditions are given in the form of linear operator inequalities (LOIs) where the decision variables are operators in Hilbert space, and the stability properties depend on switching rule. Being applied to heat switched propagation equations, these LOIs are reduced to standard Linear Matrix Inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed result.

Delay-Dependent Synchronization for Complex Dynamical Networks with Interval Time-Varying and Switched Coupling Delays

We investigate the local exponential synchronization for complex dynamical networks with interval time-varying delays in the dynamical nodes and the switched coupling term simultaneously. The constraint on the derivative of the time-varying delay is not required which allows the time delay to be a fast time-varying function. By using common unitary matrix for different subnetworks, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when subnetworks are synchronizable and nonsynchronizable, a delay-dependent sufficient condition is derived and formulated in the form of linear matrix inequalities (LMIs) by average dwell time approach and piecewise Lyapunov-Krasovskii functionals which are constructed based on the descriptor model of the system and the method of decomposition. The new stability condition is less conservative and is more general than some existing results. A numerical example is also given to illustrate the effectiveness of the proposed method.

Decentralised H ∞ filtering of interconnected discrete-time fuzzy systems with time delays

This article considers the decentralised H ∞ filtering of interconnected discrete-time fuzzy systems with time delays based on piecewise Lyapunov–Krasovskii functionals. The fuzzy system consists of J interconnected time-delay discrete-time Takagi–Sugeno fuzzy subsystems and the decentralised H ∞ filter is designed for each subsystem. It is shown that the stability with H ∞ performance of overall filtering error system can be established if a piecewise Lyapunov–Kroasovskii functional can be constructed, and moreover, the functional can be obtained by solving a set of linear matrix inequalities that are numerically feasible. A simulation example is given to show the effectiveness of the presented approach.

Generalized H&lt;sub&gt;2&lt;/sub&gt; Filtering for Discrete-Time Switched Systems with Multiple Time-Varying Delays

The generalized H2 filtering problem is investigated for linear discrete-time switched systems with multiple time-varying delays. By constructing the piecewise Lyapunov-Krasovskii functionals, employing Jensen inequality and slack variables, the delay-dependent sufficient conditions are derived for the filter-error system to be stable with a H2 performance. Based on the established results, the filter design method is presented in terms of the linear matrix inequalities (LMI). The design procedure is brief and easy to compute. The optimal filter can be solved with LMI toolbox of MATLAB directly. Finally, the simulation results illustrate the effectiveness and feasibility of the proposed method.

Delay-dependent fuzzy static output feedback control for discrete-time fuzzy stochastic systems with distributed time-varying delays

This paper is concerned with the delay-dependent H∞ fuzzy static output feedback control scheme for discrete-time Takagi–Sugeno (T–S) fuzzy stochastic systems with distributed time-varying delays. To begin with, the T–S fuzzy stochastic system is transformed to an equivalent switching fuzzy stochastic system. Then, based on novel matrix decoupling technique, improved free-weighting matrix technique and piecewise Lyapunov–Krasovskii function (PLKF), a new delay-dependent H∞ fuzzy static output feedback controller design approach is first derived for the switching fuzzy stochastic system. Some drawbacks existing in the previous papers such as matrix equalities constraint, coordinate transformation, the same output matrices, diagonal structure constraint on Lyapunov matrices and BMI problem have been eliminated. Since only a set of LMIs is involved, the controller parameters can be solved directly by the Matlab LMI toolbox. Finally, two examples are provided to illustrate the validity of the proposed method.

Robust synchronization of complex switched networks with parametric uncertainties and two types of delays

SUMMARYIn this paper, a complex switched network (CSN) with parametric uncertainties and two types of time‐varying delays is presented. The CSN contains switching behaviors on both its nodes and the network topology. Different from those CSNs studied in the literatures, the switching mode dominating the nodes systems is independent with that dominating the network topology. The two types of time‐varying delays are the system delay in the node and the coupling delay between nodes and they have different values. The inherent synchronization properties of the CSN were investigated not subject to any controllers, and sufficient conditions for the global robust exponential synchronizations are obtained by defining a piecewise Lyapunov–Krasovskii function. Both the case with known derivative of delays and the case with unknown or nonexistent derivative of delays are investigated. Two special cases, i.e. the network without coupling delay and the network without switching behaviors and coupling delay, are studied. Illustrated examples are presented to show the effectiveness of the proposed methods. Copyright © 2011 John Wiley &amp; Sons, Ltd.