Persistent Dwell-time Switching Research Articles

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.

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.

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 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.

Guaranteed H∞ Performance of Switched Systems with State Delays: A Novel Low-Conservative Constrained Model Predictive Control Strategy

In this paper, for the first time, a simultaneous design of a model predictive control plan and persistent dwell-time switching signal utilizing the conventional multiple Lyapunov–Krasovskii functional is proposed for linear delayed switched systems that are affected by physical constraints and exogenous disturbances. The conventional multiple Lyapunov–Krasovskii functional with a ‘jump high’ condition is used as a step forward to reduce the strictness of constraints on controller design compared with the switched Lyapunov–Krasovskii functional. However, a dwell-time constraint is inflicted on the switching signal by the ‘jump-high’ condition. Therefore, to decrease the dwell-time limit, the persistent dwell-time structure is used and compared with other structures. Also, a new online framework is proposed to reduce the number of constraints on controller design at each time step. Moreover, for the first time, exogenous disturbances are considered in the procedure of MPC design for delayed switched systems, and non-weighted H∞ performance is ensured. The simulation outcome demonstrates the great performance of the suggested plan and its ability to asymptotically stabilize the switched system.

New stability results for discrete-time switched systems under admissible edge-dependent average persistent dwell-time or admissible edge-dependent persistent dwell-time switching

This paper is devoted to the stability analysis of a class of discrete-time switched systems under newly designed switching regularities. The utilized switching is extended from the primitive mode-dependent persistent dwell-time switching. By integrating the existing admissible edge-dependent average dwell-time switching into the mode-dependent persistent dwell-time regime, a novel admissible edge-dependent average persistent dwell-time strategy involving the notion of admissible transition edges is proposed. The integrated admissible edge-dependent average dwell-time switching has been confirmed to be superior to mode-dependent average dwell-time switching. This superiority makes the proposed switching more general than the relaxed mode-dependent persistent dwell-time switching in the literature. Even if the embedded admissible edge-dependent average dwell-time restrictions degrade to admissible edge-dependent dwell-time ones under special parameter settings, the resulting admissible edge-dependent persistent dwell-time switching retains the advantage of admissible transition edges to generalize the original mode-dependent persistent dwell-time switching. Meanwhile, to remove the switching information reliance in the existing multiple convex Lyapunov functions, an improved multiple convex Lyapunov function method is devised. The designed Lyapunov function can be used to implement broader feasible ranges and tighter lower bounds of admissible edge-dependent average persistent dwell-time (or admissible edge-dependent persistent dwell-time). Finally, the validity and efficiency of the presented approaches are illustrated by a three-phase inverter and a numerical example.

A new $ H_{\infty} $ control method of switched nonlinear systems with persistent dwell time: $ H_{\infty} $ fuzzy control criterion with convergence rate constraints

<p>This study aims to explore the problem of $ H_{\infty} $ fuzzy control with an adjustable convergence rate for switched nonlinear systems with time-varying delays under the persistent dwell time (PDT) switching. Compared to the widely studied dwell time (DT) switching or average dwell time (ADT) switching in existing literature, PDT switching provides a more comprehensive consideration of the switching frequency and has a broader range of applicability. Subsequently, by combining the interval stability definition, T-S fuzzy model, PDT technique, and Lyapunov-Krasovskii (L-K) functional, a new $ H_{\infty} $ fuzzy control criterion for adjusting the convergence rate of switched nonlinear systems with time-varying delays is proposed. This criterion enables the development of a novel method for constructing $ H_{\infty} $ fuzzy controllers, which can regulate the system's convergence rate and achieve the specified $ H_{\infty} $ performance. Combining the above methods, an algorithm is introduced to precisely control the convergence rate of the target system. Finally, the effectiveness of this method is validated through a control example of a single-link robot arm.</p>

Fault estimation for persistent dwell time switched systems with actuator and sensor faults

This paper investigates the fault estimation (FE) problem for a class of switched systems with external disturbances, actuator faults and sensor faults. A new adaptive FE observer is proposed to estimate the sensor and actuator faults simultaneously. Meanwhile, a more general and flexible persistent dwell time (PDT) switching signal is utilized to depict slow switching and fast switching phenomenon of switched systems. Then, sufficient conditions can be achieved to guarantee the stability of the estimation error dynamics. Finally, a simulation example of the circuit system is presented to show the effectiveness of the proposed FE scheme.

Non-fragile output-feedback control for time-delay neural networks with persistent dwell time switching: A system mode and time scheduler dual-dependent design

This paper is concerned with non-fragile output-feedback control for time-delay neural networks with persistent dwell time (PDT) switching in a continuous-time setting. The main purpose is to design an output-feedback controller subject to gain fluctuations, guaranteeing both asymptotic stability and L2-gain of the closed-loop control system. To achieve reduced conservatism, the controller is formulated to depend not only on the system mode but also on a time scheduler constructed based on the PDT switching rule and minimum time span. A criterion for the asymptotic stability and L2-gain analysis is established through the application of the Gronwall–Bellman inequality and mathematical induction. Then, a numerically tractable design approach for the desired controller is proposed, utilizing a four-section piecewise time-dependent Lyapunov–Krasovskii functional and several nonlinearity decoupling techniques. For comparative purposes, a simple case, independent of the time scheduler, is also investigated, and the corresponding controller design approach is presented. Finally, a simulation example is given to illustrate the effectiveness and superiority of the proposed system mode and time scheduler dual-dependent controller design approach.

H∞ filtering for discrete-time cyclic switched systems: Relaxed cycle-dependent persistent dwell-time constraints with averaging treatment

This note investigates the H∞ filtering for a kind of discrete-time switched systems ruled by cyclic switching regularities. By virtue of the cyclic manipulation of dwell-time (DT) switching and average dwell-time (ADT) switching reported in the literature, an innovative switching strategy of cycle-dependent persistent dwell-time (CPDT) property is first developed referring to the original persistent dwell-time (PDT) scheme. Further, to overcome the cycle-dependent DT constraint appearing in the CPDT switching, cycle-dependent ADT is sub-regionally injected into the suffering areas, which is different from the full-regional injection of ADT into the PDT switching in the literature. In this way, the CPDT switching is advanced to the cycle-dependent average persistent dwell-time switching, which can bring more flexibility to the switching design. Based on the newly introduced switching mechanisms, quasi-time-dependent (QTD) stability and l2-gain criteria are formulated for discrete-time cyclic switched systems to guide the design of intended QTD full-order filters, through which the produced filter error systems perform as expected in terms of the stability and H∞ noise attenuation capability. At last, the validities and advantages of the obtained filtering solutions are expounded by specific illustrative examples.

Asynchronous Sliding Mode Control for Nonlinear Markov Jumping Systems With PDT-Switched Transition Probabilities

This paper studies the asynchronous sliding mode control for nonlinear Markov jump systems (NMJSs), whose transition probabilities is piecewise-constant and subjected to the persistent dwell-time (PDT) switching rule. By resorting to the interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy set theory, the nonlinearity and uncertainty features of the investigated systems are modeled. Taking the uncertain membership functions (MFs) of IT2 T-S fuzzy systems into consideration, the non-parallel distributed compensation strategy is employed for designing the MFs of the controller such that them do not need to be obtained in time. Furthermore, in view of the difficulty of accurately acquiring the mode of NMJSs with complex transition probabilities, the hidden Markov model is employed to provide a detected mode for constructing the sliding mode law. Afterwards, a novel fuzzy sliding surface is proposed, and an asynchronous IT2-fuzzy-model-based sliding mode control law is designed for forcing the closed-loop systems to move on the predefined sliding surface. Thereafter, a novel two-mode-dependent Lyapunov-like function is conceived for the studied systems, where modes of NMJSs and transition probabilities are permitted to change simultaneously. Through applying an improved technique to handle the parametric matrix inequalities, some less-conservative sufficient conditions in the form of linear matrix inequality are obtained for ensuring the stochastic exponentially asymptotical stability of the sliding mode with <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> performance. Finally, a mass-spring mechanical system is presented to substantiate the validity of the proposed main results.

Nonfragile observer-based event-triggered fuzzy tracking control for fast-sampling singularly perturbed systems with dual-layer switching mechanism and cyber-attacks

This paper investigates the problem of nonfragile observer-based tracking control for a class of fuzzy fast-sampling singularly perturbed systems (SPSs) with sensor saturation, which subject to event-triggered scheme and random cyber-attacks. The switching topology of the fast-sampling SPSs is dominated by a dual-layer switching mechanism, in this case, the Markov process in the underlying system is nonhomogeneous and its time-varying transition probabilities (TPs) are governed by a persistent dwell-time switching signal. First, in order to avoid asynchronous phenomenon of premise variable between the fuzzy fast-sampling SPSs and the fuzzy controller under network environments, the non-parallel distributed compensation (non-PDC) technique is applied to improve the design flexibility and reduce the conservativeness of the results. Furthermore, a novel fuzzy tracking control design scheme is proposed, in which integrating the fuzzy nonfragile observer and reference model signal into the synthetic design of the tracking controller can be expected to reduce the tracking error. Second, by constructing a well-designed time-delay and mode-dependent Lyapunov function, some sufficient conditions are derived such that the closed-loop system is mean-square exponential stable and with extended dissipative tracking performance. Finally, the effectiveness and applicability of the proposed control protocol are illustrated by two simulation examples.

Fault Reconstruction for Continuous-Time Switched Nonlinear Systems via Adaptive Fuzzy Observer Design

This paper investigates the fault reconstruction problem for a class of continuous-time switched systems subject to persistent dwell-time (PDT) switching. In order to relax the rank condition of the perturbations' coefficient matrices in fuzzy fault reconstruction results, a novel adaptive fuzzy design approach is developed by decomposing the perturbations into virtual faults and states. Then, the PDT switching is first considered in the adaptive fuzzy observer to overcome the restricted switching frequency problem, which can guarantee the stability of the estimation error systems with fast and slow switching characteristics simultaneously. Moreover, the unknown nonlinearities, actuator faults and disturbances can be reconstructed by the designed adaptive mechanism, where the switching problem of sliding surfaces in sliding mode observers can be avoided. Finally, a circuit system example is provided to demonstrate the effectiveness of the fault reconstruction scheme.

Extended Mode-Dependent Persistent Dwell-Time Switching With Multi-Stage Dependent Modification or Averaging for Discrete-Time Switched Systems

In this brief, extended mode-dependent persistent dwell-time (EMDPDT) switching with the slow-and fast-switching areas of the mode-dependent feature, where subsystems separately run for not less and less than the MDPDT, is presented for a class of discrete-time switched systems (DTSSs). The existing MDPDT is shown to be a special case of the proposed EMDPDT. Further, to loosen the dwell-time restriction on slow-switching areas in the original MDPDT regularity, two novel principles of multi-stage dependent modification (MSDM) and multi-stage dependent averaging (MSDA) are launched. By means of MSDM (or MSDA), stability criteria are supplied for DTSSs under the EMDPDT switching, where smaller MDPDT lower bounds can be achieved for non-first stages (or partially random stages) in divided units formed by multiple stages. Meanwhile, at the cost of computation consumption, MSDM allows a lower total dwell-time restriction than MSDA. Finally, the efficiency and flexibility of EMDPDT with MSDM/MSDA are illustrated by an inverter example, which indicates the predictable applicability of the presented switching for practical switched applications.

Optimal tracking control for discrete‐time modal persistent dwell time switched systems based on Q‐learning

SummaryBased on the Q‐learning, this paper investigates the tracking problem for linear discrete‐time modal persistent dwell time switched systems. The modal persistent dwell time switching rule is introduced to coordinate the switching conditions of each switching subsystems. Moreover, two algorithms are given to realize the optimization of switched systems. Then, the stability and convergence are proved. Finally, a numerical simulation example and a practical example with an electro‐hydraulic system are given to verify the effectiveness of the proposed approach.

Hysteresis quantified control for switched reaction–diffusion systems and its application

This article addresses the exponential input-to-state stabilization problem for switched reaction–diffusion systems, in which the systems’ mode jumping complies with the persistent dwell-time switching mechanism. On the basis of point measurement, a novel pointwise controller is designed to reduce the amount of sensors and actuators. Then, a hysteresis quantizer with an adjustable parameter is employed to balance the quantitative effect and system’s performance, which can improve the bandwidth utilization of the network, simultaneously. Finally, the effectiveness of the proposed approach is demonstrated by an application of the temperature control of power semiconductor chips.

Non-Fragile H∞ Synchronization for Markov Jump Singularly Perturbed Coupled Neural Networks Subject to Double-Layer Switching Regulation.

This work explores the H∞ synchronization issue for singularly perturbed coupled neural networks (SPCNNs) affected by both nonlinear constraints and gain uncertainties, in which a novel double-layer switching regulation containing Markov chain and persistent dwell-time switching regulation (PDTSR) is used. The first layer of switching regulation is the Markov chain to characterize the switching stochastic properties of the systems suffering from random component failures and sudden environmental disturbances. Meanwhile, PDTSR, as the second-layer switching regulation, is used to depict the variations in the transition probability of the aforementioned Markov chain. For systems under double-layer switching regulation, the purpose of the addressed issue is to design a mode-dependent synchronization controller for the network with the desired controller gains calculated by solving convex optimization problems. As such, new sufficient conditions are established to ensure that the synchronization error systems are mean-square exponentially stable with a specified level of the H∞ performance. Eventually, the solvability and validity of the proposed control scheme are illustrated through a numerical simulation.

Transition-Dependent Bumpless Transfer Control Synthesis of Switched Linear Systems

This technical article is concerned with the bumpless transfer control synthesis of a class of discrete-time switched linear systems with general persistent dwell-time (PDT) switching signals. A novel piecewise transition-dependent controller facilitating the control synthesis is designed, which ensures the stability of the closed-loop system as well as the bumpless transfer at the occurrence of the switching. By imposing the given bumps limitation constraints, sufficient conditions on the existence of the controller are developed for the nominal systems. The results are extended to the case of the disturbed systems with an ensured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{2}$</tex-math></inline-formula> -gain. Numerical examples are provided to demonstrate the effectiveness and potential of the theoretical results.

Event‐triggered stabilization of switching systems with persistent dwell time by dynamic quantization

AbstractThe event‐triggered stabilization of switching systems with persistent dwell time (PDT) by dynamic input quantization is addressed in this paper. The co‐design of the event‐triggered mechanism, zoom variable, PDT switching condition is achieved to eliminate the effect of asynchrony and quantization errors on stability. First, based on PDT properties and event‐triggered instants, the updated law of the zoom variable is designed and the corresponding parameters are obtained by linear matrix inequalities (LMIs). Since the PDT switching contains fast switching, which allows frequent switching within a triggered interval, detailed information on the system state is challenging to obtain. Hence, the asynchrony of system and controller modes in the stability analysis is considered. Then, the existence of a common lower bound for the triggered interval is proposed, thus eliminating the Zeno behavior. Finally, the numerical simulation verifies the validity of the method.