Dwell Time Switching Research Articles

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.

Relaxed Stability and Non-weighted $$L_2$$-Gain Analysis for Asynchronously Switched Polynomial Fuzzy Systems

AbstractThis paper concerns the stability and non-weighted $$L_2$$ L 2 -gain analysis issues for the switched systems subject to asynchronous switching and external disturbance. By taking full advantage of the admissible edge-dependent average dwell time (AED-ADT) switching signal, a stability criterion of asynchronously switched systems is proposed to achieve a lower non-weighted $$L_2$$ L 2 -gain index than the existing results. Furthermore, the dynamics of switched systems are described by using the polynomial fuzzy model instead of the T-S fuzzy model, which can represent a wider range of nonlinear plants. For such asynchronously switched polynomial fuzzy systems, the relaxed conditions are derived through the membership-function-dependent (MFD) technique and novel high-order multiple Lyapunov functions (MLFs) construction method to guarantee less conservative stability and non-weighted $$L_2$$ L 2 -gain results. Finally, the superiority of the proposed approaches are verified through two simulation examples.

Almost Sure Stability and Stabilization of Composite Switched Systems With Persistent Dwell Time Constraint.

This article is devoted to the exponential almost sure (EAS) stability and stabilization of continuous-time composite switched systems (CSSs) by employing a novel dual-switching mechanism, which incorporates both persistent dwell time (PDT) switching and a set of Markov processes. The interrelation between the parameters under the PDT constraint is established by ensuring that switching frequency remains within the maximum permissible range, which serves as a pivotal consideration in the stability analysis of CSSs subject to above-mentioned dual-switching mechanism. Furthermore, the sufficient conditions for achieving EAS-stability and stabilization of CSSs are established with the designed switching strategy. Our results, in contrast to previous works that are special cases of our study, are more general and less conservative. Three examples are presented to validate the developed theoretical results.

Input-to-State Stability of Switched Network Control Systems Under Unknown Deception Attacks.

This article focuses on the stability issue of switched network control systems (SNCSs) under deception attacks described by a Bernoulli process with unknown probability distribution. The false information in deception attacks is unknown but bounded and may be state dependent or state independent. By means of the input-to-state stability (ISS) tool and the convex combination method, an improved lemma is first developed for SNCSs, which facilitates the derivations of our results. After that, some attack-independent sufficient conditions for the ISS of SNCSs are obtained for mode-dependent average dwell time switching and stochastic switching, respectively. Different from existing results, the concerned switching contributes to the stability of SNCSs, which benefits the ISS performance of SNCSs even though the unknown deception attacks cause all subsystems to be non-ISS. The proposed results provide an effective solution with strong robustness to deal with unknown deception attacks or denial-of-service attacks.

Event-triggered adaptive bounded control of high-order uncertain switched nonlinear systems with full-state time-varying constraints

ABSTRACT In this article, an adaptive event-triggered bounded control strategy is proposed for a class of high-order uncertain switched nonlinear systems with full-state time-varying constraints under average dwell time switching rule. In order to achieve the boundedness of the control signal, the projection operator is introduced. At the same time, the high-order log-type time-varying barrier Lyapunov function method is chosen to ensure that the desired output and states of the systems do not violate the relevant constraints. In addition, the improved event-triggered control strategy effectively reduces the transmission burden and saves the resource cost. The stability analysis shows that the proposed scheme achieves the ultimate boundedness of all signals in the closed-loop systems and the states of the systems do not violate the corresponding constraints. It should be noted that the proposed controller has a known bound and this bound can be ensured by the rectification of the feedback control gain. Finally, the simulation results verify the effectiveness of the control method.

Event-triggered quasi-time-varying [formula omitted] filtering for switched systems via multiple trigger-dependent Lyapunov functionals

This paper investigates the event-triggered filtering problem for switched systems from the perspective of switched impulsive systems (SISs) by exploiting the characteristics of trigger and impulse behavior. By constructing multiple trigger-dependent Lyapunov functionals (MTDLFs), an event-triggered quasi-time-varying (ET-QTV) H∞ filtering scheme is developed. Since the MTDLFs properly capture the event-induced impulse property of SISs, they release less conservatism. The filtering stability in the scenario of frequent plant switching during an interevent interval is also guaranteed by incorporating the average dwell time switching. The filtering synthesis condition is formulated as a set of QTV matrix inequalities defined over a finite time horizon, based on which a sum of squares-based filter design algorithm is presented further. Additionally, the derivation of a lower bound on interevent intervals is clarified for the event-triggering mechanism (ETM) to exclude the Zeno phenomenon. Finally, the effectiveness and potential practicability of the proposed filtering scheme are validated using a morphing aircraft model.

Output Reachable Set-Based Leader-Following Consensus of Positive Agents Over Switching Networks.

This work addresses the output reachable set-based leader-following consensus problem, focusing on a group of positive agents over directed dwell-time switching networks. Two types of non-negative disturbances, namely, 1) L1 -norm bounded disturbances and 2) L∞,1 -norm bounded disturbances are studied. Meanwhile, a class of directed dwell-time switching networks for modeling the communication protocol of positive agents is investigated. To deal with the presence of disturbances, an output-feedback control protocol is developed to achieve a robust consensus with positivity preserved based on the output reachable set. By exploiting the positive characteristics, switched linear copositive Lyapunov functions are adopted to establish output reachable set-based consensus conditions. These conditions can facilitate the control protocol design by solving a bilinear programming problem, and also generate hyperpyramidal regions to confine the output consensus error. A particle swarm optimization-based (PSO-based) algorithm is applied to compute the controller gains and optimize the volume of the hyperpyramids. The proposed methods are verified by the presented numerical case studies.

Semi-time-dependent stabilization results for asynchronously switched systems: An extended persistent dwell time switching strategy involving admissible transition information

This study investigates the stabilization problem for a kind of continuous-time asynchronously switched systems via a set of edge- or mode-dependent state-feedback controllers. To this end, an innovative switching strategy of admissible chain-dependent (or admissible edge-dependent) persistent dwell time property is presented by injecting the admissible transition chain (or admissible transition edge) notion into the existing persistent dwell time concept. Based on the admissible transition edges in a directed graph reported in the literature, the corresponding admissible transition chains can be determined. The individual allocation of transition weights for each admissible transition chain makes the presented admissible chain-dependent persistent dwell time switching less conservative than the other presented admissible edge-dependent persistent dwell time and the already existing mode-dependent persistent dwell time switching. Further, different from the Lyapunov functions commonly used in previous asynchronous stabilization works, a new semi-time-dependent Lyapunov function in a unique form that fits the nature of the discussed systems is suggested to provide a broader family of allowable switching signals. By the introduced switching and Lyapunov function approaches, new stability and stabilization criteria are formulated, through which the expected edge- or mode-dependent state-feedback controllers are devised. At last, the validity and applicability of the obtained stabilization solutions are demonstrated by a numerical example and a practical thermal system.

Dynamic output feedback based fault tolerant control for continuous-time switched affine systems via reduced-order observer

In this study, the issue on dynamic output feedback fault-tolerant controller design is addressed for a class of continuous-time switched affine systems in the presence of actuator faults. The existence of affine terms gives rise to the lack of a common equilibrium point and further makes it more difficult to propose the desired output-feedback-based fault-tolerant control scheme. Firstly, the actuator fault estimation is achieved through a reduced-order observer design approach. Then, a kind of dynamic output feedback controller is constructed to perform the fault tolerance goal by utilizing fault estimation information. Moreover, the mode-dependent average dwell time switching constraint is borrowed to avoid the chattering owing to the high-frequency switching. The sufficient conditions with less conservative are derived to guarantee the practical exponential stability of closed-loop system with a prescribed L∞ gain. Finally, both the effectiveness and validity of the designed fault-tolerant control strategy are illustrated via a case study of a buck-boost DC-DC converter.

Dynamic event-triggered asynchronous control for switched T-S fuzzy systems

The H∞ control problem for a class of continuous-time switched Takagi-Sugeno (T-S) fuzzy systems with mode-dependent average dwell time (MDADT) switching rules is the main topic of this article. Firstly, the transmission burden is relieved by efficiently reducing the number of signal transmissions by the application of a revolutionary dynamic event-triggered mechanism (ETM). Secondly, there is a thorough understanding of the dynamic event-triggered, asynchronous control behaviors that exist between the controllers and subsystems. To ensure H∞ performance of the asynchronous switched T-S fuzzy systems, certain appropriate adequate circumstances are derived by using the merged switching signal approach and Lyapunov-like functional (LKF) method. Lastly, a practical and an numerical example demonstrate the viability and implementation of the conclusions gained.

Protocol-based state estimation of two-time-scale complex networks with nonhomogeneous sojourn probabilities

This paper is dedicated to researching the problem of the state estimation for two-time-scale complex networks (TTSCNs) subject to sojourn probabilities (SPs) under channel fadings and false data injection attacks (FDIAs). The network’s switching topology is governed by a novel switching law that incorporates time-varying SPs, with the variation of SPs being regulated through a persistent dwell-time (PDT) switching signal. Meanwhile, for the sake of achieving energy savings and mitigating data congestion, the dynamic probabilistic event-triggered weighted try-once-discard (DPEWTOD) policy is innovatively developed by integrating with the major merits of the dynamic probabilistic event-triggered mechanism (DPETM) and WTOD protocol (WTODP) based on hybrid compensation. Different from the traditional communication rules, this DPEWTOD concept not only captures stochastic behavior of the dynamic triggering threshold (DTT), but also enables a compensatory measurement that closely approximates the actual value. Subsequently, we construct time delay-, DTT-, and PDT-dependent Lyapunov functionals to analyze the stability of error dynamic systems in the presence of fading and malicious FDIAs. By employing a separation technique, our proposed solving algorithm transforms non-convex analysis conditions into tractable ones. Eventually, the rationality and effectiveness of the proposed method are demonstrated by an resistance–capacitance (RC) circuit example.

Switching Anti-Windup Synthesis for Linear Systems With Asymmetric Actuator Saturation.

This article proposes a switching anti-windup strategy for linear, time-invariant (LTI) systems subject to asymmetric actuator saturation and L2 -disturbances, the core idea behind which is to make full use of the available range of control input space by switching among multiple anti-windup gains. The asymmetrically saturated LTI system is converted to a switched system with symmetrically saturated subsystems, and a dwell time switching rule is presented to govern the switching between different antiwindup gains. Based on multiple Lyapunov functions, we derive sufficient conditions for guaranteeing the regional stability and weighted L2 performance of the closed-loop system. The switching anti-windup synthesis that designs a separate anti-windup gain for each subsystem is cast as a convex optimization problem. In comparison with the design of a single anti-windup gain, our method can induce less conservative results since the asymmetric character of the saturation constraint is fully utilized in the switching anti-windup design. Two numerical examples, and an application to aeroengine control (the experiments are conducted on a semiphysical test bench), demonstrate the superiority and practicality of the proposed scheme.

Quantized filtering for switched memristive neural networks against deception attacks

This paper deals with the quantized mixed H∞/L2−L∞ filtering issue for switched memristive neural networks in the presence of deception attacks, in which the switching of parameters is not only subject to neural states, but also to the persistent dwell-time switching rule in the continuous-time case. First, a switched dynamic quantizer is utilized to quantize the measurement output before being transmitted to the filter. Second, deception attacks governed by a Bernoulli distribution are considered during the quantized output transmission. Then, in virtue of the Lyapunov stability theory together with stochastic analysis theory, a sufficient condition is given to ensure the global uniform asymptotic stability in the mean-square sense for the filtering error system with a mixed H∞/L2−L∞ performance. Furthermore, a co-design scheme for the desired mode-dependent filter gain and dynamic parameter is provided. Ultimately, the effectiveness of the proposed method is verified by a numerical example.

Coding–decoding-based synchronization of Markov jump neural networks with PDT switched topologies

This paper investigates the observer-based synchronization control issue for a class of discrete-time switched neural networks under the constraint that information exchange between the observer and controller is subject to coding–decoding communication protocol. The variation of network parameters is governed by a Markov chain while a set of pre-known persistent dwell-time switching sequence is introduced to describe the variation of communication topologies among neurons. To ensure the efficient and secure of information transmission, data received from the observer is encoded into a particular set of codewords before sending to the communication channel. Then, these codewords are transformed into corresponding decoded form via the designed decoder after transmission. The main attention is focused on devising a feasible coding–decoding procedure such that the coding–decoding-based controller can be established efficiently. By constructing suitable Lyapunov function that can reveal the variation characteristic of the network parameters and topologies properly, sufficient conditions which ensure the exponential mean-square boundedness of the closed-loop synchronization error systems are presented. Finally, the validity of the proposed control scheme is illustrated by a numerical example.

Stability analysis and stabilization control of discrete-time impulsive switched time-delay systems with all unstable subsystems

n this paper, stability analysis and stabilization control of discrete-time impulsive switched time-delay systems with all unstable subsystems are discussed. By utilizing a switching time-varying Lyapunov–Krasovskii functional and the mode-dependent interval dwell-time switching rule, we derive some more general stability theorems for the considered time-delay system with all subsystems being unstable. Moreover, we design a time-varying state feedback controller to ensure the stabilization of the resulting closed-loop system. Eventually, the theoretical findings are demonstrated utilizing numerical examples.

Bumpless transfer control for switched impulsive positive systems with [formula omitted]-gain performance

This paper investigates the problem of bumpless transfer control for switched impulsive positive systems with L1-gain performance. For switched impulsive positive systems, the control bump is brought from both switching behavior and impulsive effects. First, the concept of bumpless transfer performance is proposed by imposing magnitude constraints on the control signal to measure the level of bumpless transfer in the switched impulsive positive system. Then, based on a new class of multiple piecewise-continuous copositive Lyapunov function, a tighter mode-dependent average dwell time switching signal bound and bumpless transfer controller are designed to realize positive property, bumpless transfer and L1-gain performance of the closed-loop systems. Finally, the feasibility and superiority of the proposed control strategy are illustrated by simulations.

Stability and unweighted L1-gain analysis for switched time-delay positive systems with stable and unstable subsystems

This article investigates the stability and unweighted L1-gain analysis of switched time-delay positive systems (STDPSs) with stable and unstable subsystems. The persistent dwell time (PDT) switching is considered for the first time, which is more general compared with the typical dwell time (DT) or average dwell time (ADT) techniques. Under the PDT switching, the activation time of an unstable subsystem is less than an upper bound instead of greater than a given constant, which makes it easier to achieve stability in practice. Considering the stable and unstable subsystems, a piecewise multiple co-positive Lyapunov–Krasovskii functional is constructed to obtain the stability criterion of the STDPSs. Subsequently, the unweighted L1-gain for STDPSs is explored, which has explicit physical meaning compared with the weighted results and can be calculated by solving the linear programming problem. Finally, a water-quality model and a numerical example are provided to indicate the validity of the proposed methods.

Mean square exponential stability with l2−l∞ gain of discrete-time switched-Markovian jump systems

In this paper, the problem of mean square exponential stability with [Formula: see text] gain is studied for the discrete-time switched-Markovian jump systems, which are composed of a deterministic switched system and a Markovian jump system. The mode-dependent average dwell time method is adopted to design the switching signal for the deterministic switched system, and the Markovian jump property is presented by the Markov chain, which is dependent on the designed mode-dependent average dwell time switching signal. The multiple discontinuous Lyapunov function is constructed to guarantee the mean square exponential stability and [Formula: see text] performance. Furthermore, a novel inequality is established to show the relationship between multiple discontinuous Lyapunov functions and disturbances to derive the [Formula: see text] performance. Finally, two numerical examples and a circuit system are given to demonstrate the effectiveness of the obtained results.

Event-triggered H∞ control for switched systems based on interval observer

The paper studies the design of interval observer–based event-triggered [Formula: see text] controller for switched systems with frequent asynchronism. We first propose an interval observer–based event-triggered mechanism, which is used to transmit the observer states and the activated mode information for controller updating. Then, we design an interval observer–based event-triggered [Formula: see text] controller for the considered systems. By using the controller mode–dependent Lyapunov function method, sufficient conditions for the globally exponential stability of the closed-loop switched systems are obtained under average dwell time switching law. Moreover, we prove that the interevent interval length is a positive constant, which can exclude the Zeno behavior. Compared with the literature, the paper removes the strict requirement of at most one switch between two event-triggered instants, that is, frequent switches within an interevent interval are allowed. Finally, a numerical example is given to verify the effectiveness of the proposed method.

Simultaneous fault-tolerant control and disturbance rejection for impulsive switched systems

This paper considers the simultaneous fault-tolerant control and disturbance rejection of impulsive switched linear systems. First, estimates of faults and disturbances in the system can be obtained by designing observers. Then, through the obtained estimation, the controller with anti-interference performance and fault tolerance performance is designed. Under the arbitrary switching rules and the minimum dwell time switching rules, the stability of the system is guaranteed. Finally, the effectiveness of the method is verified by numerical simulation and example simulation.