Switched Lyapunov Function Research Articles

Probability‐Based Finite‐Time Security Control for Switched Stochastic Systems via a Novel Event‐Triggered Mechanism and Its Application

ABSTRACTThis article discusses the finite‐time boundedness (FTB) issue and ‐gain analysis for switched stochastic systems, particularly under the dual influence of DoS attacks and false data injection attacks, by employing a novel event‐triggered mechanism. Different from the moment calculation method, a probability‐based FTB is studied which offers more pertinence. To obtain a less conservative condition of FTB, a switched Lyapunov function is constructed. Additionally, a memory‐based dynamic event‐triggered mechanism is designed to reduce the amounts of triggering and mitigate the state response fluctuations. Based on the incomplete information above, state feedback controllers are devised to satisfy stochastic FTB, ensuring the successful attainment of finite‐time ‐gain. Sufficient conditions are cast into a convex optimization problem by LMIs which can be solved easily. Finally, a compared numerical example and an RLC series circuit are adopted to demonstrate the availability of the theoretical results.

Stability analysis and stabilization of discrete-time switched nonlinear systems with mode-dependent average dwell time under nested actuator saturation

In this paper, the stability analysis and stabilization of a class of mode-dependent mean residence time-based discrete-time switching nonlinear systems are addressed. More specifically, under the mode-dependent average dwell time (MDADT) switching mode, combined with the practical problem, the nonlinear factor of nested actuator saturation (NAS) is introduced. Firstly, in order to ensure the system stability, based on the parameter-dependent discontinuous switching Lyapunov function and several basic lemmas, a state feedback controller is designed that makes the closed-loop system (CLS) achieve local exponential stability (LES) by solving the optimal problem in terms of linear matrix inequalities (LMIs). Secondly, the system considers the maximum attraction domain that can be achieved by the NAS system under the conditions. The simulation results show the effectiveness of the proposed design method. At the same time, the efficiency of the proposed method is verified via a water tank example.

L2-gain analysis and fault-tolerant control of nonlinear discrete time-delay saturated switched systems with memory state feedback

For nonlinear discrete time-delay saturated switched systems with memory feedback, the problem of actuator failure with external disturbances is studied. First, we propose a sufficient condition for the existence of a fault-tolerant state feedback law with memory by using the switched Lyapunov function (SLF) strategy, which ensures that the closed-loop system has a maximum tolerant disturbance capacity by solving the optimization problem. Then, the minimum upper bound on the [Formula: see text]-gain is estimated by solving the optimization problem. Finally, the reliability of the proposed method is verified by examples.

Practical stabilisation of discrete-time switched nonlinear systems without a common equilibrium and using hybrid switching functions

This paper presents a new practical stabilization method for discrete-time switched nonlinear systems without a common equilibrium point among all modes. The proposed method has two main features. First, the number of nonlinear terms in the stability conditions is independent of the number of switched system modes. The result is that the computational cost is reduced, and it can be applied to switched systems with a large number of subsystems. Second, using switched Lyapunov functions, hybrid switching laws are designed to preserve the practical stability property in both the closed-loop state-dependent switching function and the open-loop time-dependent one. As a result, when the state data is lost during sensor or communication failures, the controller can change the control scheme from a closed-loop state-dependent switching function to an open-loop time-dependent one without loss of stability property. Numerical examples are presented to illustrate the validity and efficiency of the proposed method.

Hybrid stabilization of nonlinear systems based on a fully actuated system approach

This article studies the stabilization problem for a category of nonlinear systems. It introduces a novel hybrid control strategy specifically for nonlinear high-order fully actuated (HOFA) systems. The stabilization problem for these nonlinear HOFA systems is transformed into a stabilization problem for impulsive switched systems. This issue is addressed by applying impulsive control in discrete-time and switching control based on the HOFA system approach in continuous-time. Using switched Lyapunov functions, we obtain the criteria for the exponential and asymptotic stabilization of these systems. The effectiveness of this newly presented hybrid control strategy is exemplified by simulations of a robotic manipulator system and a reduced model of the lac operon.

Composite Switched Lyapunov Function-Based Control of DC–DC Converters for Renewable Energy Applications

Renewable energy sources play a pivotal role in the pursuit of sustainable and eco-friendly power solutions. While offering environmental benefits, they present inherent challenges. Photovoltaic systems rely on surrounding conditions, wind systems contend with variable wind speeds, and fuel cells are both costly and inefficient. Furthermore, the energy injected by renewable energy sources (RES) exhibits unpredictable behavior. To tackle these problems, researchers employ diverse power electronic devices and converters like inverters, power quality filters, and DC–DC choppers. Among these, DC–DC converters stand out for effectively regulating DC voltage and enhancing the efficiency of RESs. The meticulous selection of a suitable DC–DC converter, coupled with the integration of an efficient control technique, significantly influences overall power system performance. This paper introduces a novel approach to the design of switching controllers for DC–DC converters, specifically tailored for application in renewable energy systems. The proposed controller leverages the power of composite switched Lyapunov functions (CSLF) to enhance the efficiency and performance of DC–DC converters, addressing the unique challenges posed by renewable energy sources. Through comprehensive analysis and simulation, this study demonstrates the efficacy of the controller in optimizing power transfer, improving stability, and ensuring reliable operation in diverse renewable energy environments. Moreover, the small-scale DC–DC converter experiment’s findings are presented to confirm and validate the proposed scheme’s practical applicability.

Fault estimation of continuous‐time switched affine systems with actuator faults under dwell time constraint

SummaryThis paper investigates the problem of fault estimation for a class of continuous‐time switched affine systems with actuator faults. In most of the existing results of switched affine systems based on the min‐switching approach, the candidate Lyapunov function is usually common, such that it is conservative to derive the practical stability conditions. To overcome this restriction, a class of switched Lyapunov function is introduced to increase more degrees of freedom of the designed min‐switching strategy and to ensure the stability of error systems. At the same time, the proposed dwell‐time dependent switching strategy can avoid the frequent switchings commonly existing in the min‐switching mechanism. Then, a new intermediate estimator is designed to estimate the state and fault simultaneously, and the intermediate estimator based fault estimation is performed under the proposed mixed switching law. Moreover, the gains of fault estimator are explicitly calculated via resolving the conditions of linear matrix inequalities. Finally, two examples including a flyback DC‐DC power converter are illustrated to verify the effectiveness and advantage of proposed fault estimation approach.

Integral sliding mode control design for uncertain impulsive systems with delayed impulses

This paper addresses the integral sliding mode control (ISMC) problem of uncertain impulsive systems with delayed impulses. Firstly, an integral sliding surface with embedded impulse information is constructed, which is able to counteract the intermittent impact of delayed impulses. Then an ISMC law is designed to guarantee the finite-time reachability of the predefined sliding surface without special restriction on system dynamics. Secondly, two different types of linear control laws with switching gains are proposed to robustly stabilize the sliding mode dynamics. The first type is independent of the size of impulse delays, and is used to tackle the impulses with unknown bounded delays. The second type aims at providing impulse-delay-dependent stabilization algorithms under the assumption that the delays are smaller than the impulse intervals. In the situation where the upper bounds of the uncertainties are characterized by two unknown constants, an adaptive ISMC law is proposed to ensure the existence of sliding mode. Switching Lyapunov functions and the state augmentation technique are introduced to exploit the positive/negative effects of delayed impulses. Several tractable conditions for designing the switching gains and the sliding surfaces are derived in terms of linear matrix inequalities. Finally, three numerical examples are presented to show the effectiveness of the proposed control algorithms and highlight their merits.

Observer-Based Control for Discrete-Time Hidden Semi-Markov Jump Systems

In this note, the control problem for discrete-time hidden semi-Markov jump systems is investigated under the situation that the system modes are unavailable directly. Compared with the previous results, the case when both system modes and states are immeasurable simultaneously is fully considered and an observer-based control scheme is established for discrete-time hidden semi-Markov jump systems. The random parameters of the systems are subject to a two-layer stochastic process and the underlying stochastic process is assumed to be subject to a semi-Markov process. Furthermore, a novel switched Lyapunov function is used, which may be monotonically increasing or decreasing at the instant of non-modal switching. Moreover, by means of the stochastic stability theory and semi-Markov kernel method, some novel sufficient conditions ensuring <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sigma$</tex-math></inline-formula> -error mean-square stability of the closed-loop system are obtained by a power term reduction method. Finally, an illustrative example is introduced to verify the feasibility of the proposed control method.

Time‐regularization event‐triggeredH∞control for switched linear systems with frequent asynchronism

AbstractThis paper addresses the time‐regularization event‐triggered control problem for a class of continuous‐time switched systems with frequent asynchronism and external disturbances. In the system, both the system state and the switching information are transmitted to the controller only at the event‐triggered sampling instants, which may cause the occurrence of asynchronous switching behavior. To solve the problem, we first propose a time‐regularization event‐triggered mechanism, which not only avoids Zeno behavior efficaciously, but also allows the system to switch multiple times in the holding interval. Then, based on the time‐regularization event‐triggered mechanism, the error system is modeled as a sampled switched delay system with augmented switching signal. After that, sufficient conditions for the exponentially stability and weighted performance of the switched system under average dwell time are derived by constructing multiple switching Lyapunov functions. Finally, a circuit example is given to illustrate the effectiveness of the proposed method.

Observer-Based Dynamic Event-Triggered Tracking Consensus for Switched Multi-Agent Systems

This article discusses the event-triggered consensus problem for a switched multi-agent system (MASs) with switching topologies. An observer-based dynamic event-triggered (DET) controller with a discontinuous nonlinear term is designed to reduce arduous communication. With the designed approach, the error system can reach a tracking consensus. Then, a continuous observer-based DET protocol is created using the boundary layer method to prevent chattering effects. Moreover, by employing the Riccati equation and the switched Lyapunov function method, some sufficient criteria are put forward to guarantee the tracking consensus of the systems. The suggested observer-based DET protocol can also exclude the Zeno behavior. Finally, two examples verify the validity of the analysis.

Fully distributed event‐triggered consensus control for linear multiagent systems under DoS attacks

AbstractThis article investigates the event‐triggered consensus problem of general linear multiagent systems with denial‐of‐service (DoS) attacks. A distributed event‐triggered mechanism is presented to alleviate the limited communication resources, the designed mechanism is fully distributed owing to the introduction of some adaptive parameters. Moreover, since the DoS attacks have been considered in the event‐triggered rule design, a switching strategy for the adaptive parameters is adopted. A switching Lyapunov function is used to strictly demonstrate that secure consensus can be reached effectively under the proposed control mechanism. The quantitative relationship between the frequency of the DoS attacks and the consensus is also presented. Moreover, the Zeno behaviour can be excluded for the studied close‐looped systems. Finally, a numerical simulation example is given to demonstrate the validity of the designed control law.

Dissipative control of switched nonlinear systems with sliding mode: an event-triggered control scheme

This paper introduces the event-triggered scheme to study the problems of dissipative control and dissipativity-based sliding mode control (SMC) for switched nonlinear systems. Firstly, based on a designed event-triggered scheme, a piecewise continuous state feedback controller is constructed; sufficient conditions for $$\left( Q,S,R\right) $$ - $$\alpha $$ -dissipativity of the resulting system are derived by the approaches of a switched Lyapunov function and an average dwell time. Secondly, these two methods are extended to the study of $$H_\infty $$ performance and passive performance; the corresponding sufficient conditions are provided. Thirdly, the dissipative control problem is solved by introducing an event-triggered scheme into SMC method. Sufficient conditions for dissipativity of the resulting system are derived, and an SMC law is designed to guarantee the reachability. At the end of this paper, the correctness of the proposed methods is proved by two numerical examples.

Directed-Graph-Learning-Based Diagnosis of Multiple Faults for High Speed Train With Switched Dynamics.

This article addresses the distributed multiple fault isolation, modeling, and the closed-loop fault estimation under asynchronous switching for high speed train (HST) with switched dynamics, which is composed of traction, coasting, and braking. First, directed-graph-quantum-learning-based multiple-agent system (MAS) classifiers are introduced to characterize the joints effects of multiple faults. Some sufficient conditions are derived under the condition that the multiple fault topology contains a directed spanning tree and cycle edge, and these conditions guarantee that the multiple fault isolation problem can be solved under randomized learning techniques. Then, single-integrator agents are employed to capture the time-varying topology of multiple fault modeling, in which edge agreement and persistence condition are used to guarantee asymptotic consensus. After that, a novel robust fault estimation design along with the switched Lyapunov function and average dwell time is proposed for the possible power actuator faults subject to asynchronous switching and electromagnetic interferences. In addition, switched estimators are designed such that the closed-loop system is asymptotically stable. A multiple fault isolation and estimation case is investigated to validate the application of this methodology.

Bipartite Containment Control for Delayed Multiagent Systems With Markovian Switching Topologies Under Impulsive Attacks

This paper is concerned with the problem of bipartite containment control design for a class of nonlinear multiagent systems with time-delays in agents’ states under impulsive false-data-injection attacks. The considered multiagent system is subject to Markovian variation in the signed communication topology. The graph among the followers is assumed to be structurally balanced for each Markovian switching mode. A memory distributed control protocol is proposed to achieve bipartite containment within the convex hull of leader agents as well as the symmetric convex hull. The bipartite containment control problem is solved by means of a Markovian switching Lyapunov function and the Razumikhin technique. In addition, the problem of bipartite leader-following consensus is also addressed for delayed nonlinear multiagent systems with one leader. Two examples are provided to show the effectiveness of the proposed control scheme, and comparison results with existing methods are given as well.

Output-feedback control for discrete-time switched systems via non-monotonic switched Lyapunov function approach

This paper investigates the output-feedback control for discrete-time switched linear systems. By extending the methodology of switched Lyapunov functions (SLF), a non-monotonic SLF approach is proposed to analyse the stability of the resulting closed-loop system under arbitrary switching. This approach relaxes the requirement of monotonicity to conventional SLF approach, and hence it will lead to less conservative results. First, the stability of discrete-time switched systems is analysed, and then an output-feedback controller design method is proposed based on the obtained stability results. The controller design problem is formulated in term of LMIs, and relaxed variables are introduced in the synthesis conditions to improve the design freedom. Finally, three examples are used to verify the effectiveness and application potential of the proposed methods.

Stabilization of Logical Dynamic Networks via Event-Triggered Switching Signals and Its Application

This paper studies the stabilization of logical dynamic networks (LDNs) via event-triggered switching signals. Compared with existing results, the designed switching signal does not need to be updated at each time step, and it will greatly reduce the waste of resources in the process of information transmission. At present, most of the proposed event-triggered mechanisms (ETMs) for LDNs are available for special systems and are also difficult to implement in practice. Our goal is to propose an ETM with generality and strong operability, under which the designed switching signals can be used to stabilize the addressed system. Considering that the Lyapunov method can be successfully applied to investigating the stability of different LDNs, here we propose the concept of switching Lyapunov function and try to establish the ETM based on the switching Lyapunov function. A necessary and sufficient condition is derived from the existence of the switching Lyapunov function for the stabilization of LDNs via event-triggered switching signals. In terms of the obtained switching Lyapunov functions, two algorithms are further developed to seek the time-optimal switching sequence and cost-optimal switching sequence. Moreover, the obtained results are applied to the stabilization of LDNs with logical switching as well as impulsive LDNs. An example is finally given to show the effectiveness of the theoretical results.

Exponential Stability of Switched Neural Networks with Partial State Reset and Time-Varying Delays

This paper mainly investigates the exponential stability of switched neural networks (SNNs) with partial state reset and time-varying delays, in which partial state reset means that only a fraction of the states can be reset at each switching instant. Moreover, both stable and unstable subsystems are also taken into account and therefore, switched systems under consideration can take several switched systems as special cases. The comparison principle, the Halanay-like inequality, and the time-dependent switched Lyapunov function approach are used to obtain sufficient conditions to ensure that the considered SNNs with delays and partial state reset are exponentially stable. Numerical examples are provided to demonstrate the reliability of the developed results.

Advanced Stability Conditions for TS Fuzzy Systems via Minimum-Type Multiple Switching Lyapunov Function

This article deals with the stability analysis of TS fuzzy models using the novel minimum-type multiple switching Lyapunov function. A method is presented to investigate the stability of the model which consists of three separate steps; mesh the space of the model using the Delaunay method, considering a quadratic function for each vertex of the mesh, proposing a set of conditions based on the declared quadratic functions. The proposed conditions can be categorized into two sets; local and discontinuity conditions. The local conditions exploit the local stability in each simplex of the mesh which have minimum-type multiple forms. The discontinuity conditions force the global Lyapunov function to decrement in the switching points (boundary of the neighbor simplexes). To validate the result of the proposed approach, comparative simulation examples are given to illustrate the performance of the design methodology as compared to those of previous approaches.

Practical Stability Analysis and Switching Controller Synthesis for Discrete-time Switched Affine Systems via Linear Matrix Inequalities

This paper considers the practical asymptotic stabilization of adesired equilibrium point in discrete-time switched affine systems.The main purpose is to design a state feedback switching rule forthe discrete-time switched affine systems whose parameters can beextracted with less computational complexities. In this regard,using switched Lyapunov functions, a new set of sufficientconditions based on matrix inequalities are developed to solve thepractical stabilization problem. For any size of the switched affinesystem, the derived matrix inequalities contain only one bilinearterm as a multiplication of a positive scalar and a positivedefinite matrix. It is shown that the practical stabilizationproblem can be solved via a few convex optimization problems,including Linear Matrix Inequalities (LMIs) through gridding of ascalar variable interval between zero and one. The numericalexperiments on an academic example and a DC-DC buck-boost converter,as well as comparative studies with the existing works, prove thesatisfactory operation of the proposed method in achieving betterperformances and more tractable numerical solutions.