Average Dwell Time Method Research Articles

Polynomial stability of positive switched homogeneous systems with time delay

Based on the logarithm contraction average dwell-time method, this paper investigates the polynomial stability of positive switched homogeneous time-delay systems whose vector fields are of different degrees with respect to a dilation map. Using the analytical skills developed in positive systems, an explicit polynomial stability criterion is established for the first time for the involved system under the logarithm contraction average dwell-time switching. Moreover, the main result is applied to the polynomial stability of Persidskii-type switched systems.

Finite‐time secure state estimation for a class of switched systems subject to deception attacks

AbstractThis article is concerned with the finite‐time secure state estimation problem for switched systems subject to malicious attacks. The sensor data is considered transmissible via a non‐secure communication network environment, where the communication channel might be subject to deception attacks. By dividing the sensor data that is subject to attacks into two parts, related and unrelated to the original measurements, a switched secure state estimation error system model is established. Moreover, based on the average dwell time method, sufficient conditions are derived for the switched secure state estimation error system to be finite‐time stable, as well as finite‐time boundedness. An existence condition of the finite‐time secure state estimator gains with a desired performance is given. Subsequently, the finite‐time secure state estimator gains' design is transformed to solve a set of linear matrix inequalities. Finally, numerical examples are used in order to show the effectiveness of the proposed finite‐time secure state estimator design method.

Asynchronously finite‐time fault detection for switched systems with unstable modes and intermittent measurements

This study proposes a novel fault detection (FD) filter design approach for switched systems with unstable modes and intermittent measurement; the FD filter design approach considers asynchronous switching and ensures finite-time stability (FTS). First, a model of switched systems with undesirable communication and unstable modes is established. The FD filter is developed using the observer technique, and the conditions of FTS and H∞ performance for the above systems are proposed and verified. The multiple discontinuous Lyapunov function (MDLF) method and the mode-dependent average dwell time (DT) method are used to obtain the switching strategy, which includes fast and slow switching to address the stability of unstable and stable modes, respectively. Compared with conventional approaches, the proposed method can realize less conservative stability conditions and a more flexible design framework, providing an efficient approach for improving system performance. Finally, based on the determined FTS criteria and H∞ performance, the FD filter for switched systems is presented. Simulation results are provided to verify the effectiveness of the proposed method.

Adaptive neural control for nonlinear switched systems with improved MDADT and its applications

In this paper, a new framework of the robust adaptive neural control for nonlinear switched stochastic systems is established in the presence of external disturbances and system uncertainties. In the existing works, the design of robust adaptive control laws for nonlinear switched systems mainly relies on the average dwell time method, while the design and analysis based on the model-dependent average dwell time (MDADT) method remains a challenge. An improved MDADT method is developed for the first time, which greatly relaxes the requirements of Lyapunov functions of any two subsystems. Benefiting from the improved MDADT, a switched disturbance observer for discontinuous disturbances is proposed, which realizes the real-time gain adjustment. For known and unknown piecewise continuous nonlinear functions, a processing method based on the tracking differentiator and the neural network is proposed, which skillfully guarantees the continuity of the control law. The theoretical proof shows that the semiglobal uniform ultimate boundedness of all closed-loop signals can be guaranteed under switching signals with MDADT property, and simulation results of the longitudinal maneuvering control at high angle of attack are given to further illustrate the effectiveness of the proposed framework.

Stability of Logical Dynamic Systems With a Class of Constrained Switching

In this paper, a novel constrained switching rule, called “time-triggered logical switching” (TTLS) is considered for switched logical dynamic systems (SLDSs). Compared with the general time-triggered switching, the activation mode of TTLS cannot be arbitrary and is pre-allocated according to the logic operation, which is more practical. The TTLS is described as an LDS, and according to the characteristics of LDS, the stability analysis of SLDSs with TTLS is converted into the stability analysis of SLDSs under the logical switching cycle sequences. Firstly, based on the equivalent algebraic form of SLDSs with TTLS, combining the Lyapunov theory of LDS with average dwell-time method, several sufficient conditions are put forward for ensuring the point stability of the considered SLDSs. Then, by defining the switching cycle invariant subset and constructing a new system, the set stability analysis of the original system is transformed into the point stability analysis of the new system, and further, the obtained results for the point stability analysis are applied to the set stability analysis. At last, the validity of obtained results is illustrated by simulation on gene and protein signaling activity patterns.

Adaptive command filtered control for switched multi‐input multi‐output nonlinear systems with hysteresis inputs

SUMMARYThis article is devoted to designing an adaptive command filtered control scheme for a category of multiple‐input multiple‐output switched nonlinear systems with backlash‐like hysteresis. The “explosion of complexity” issue, which comes from the derivatives of the intermediate controller, is eliminated by using a command filter technique. Meanwhile, an error compensation mechanism is introduced to offset the filter error's impact on system performances and overcome the drawback of traditional dynamic surface control methods. Furthermore, a proper Lyapunov function and an adaptive law are fixed in the last step of the backstepping design procedure to surmount the design difficulty arising from the backlash‐like hysteresis nonlinearity. In a word, by utilizing the command filter technique, backstepping algorithm, and average dwell time method, an adaptive controller is constructed, which can not only guarantee that the system outputs track the desired trajectories as far as possible but also ensure all the signals are bounded. Simulation results are provided to illustrate the effectiveness of the proposed scheme.

Fuzzy Adaptive Output Feedback Fault-Tolerant Control for Nonlinear Switched Large-Scale Systems With Sensor Faults

To handle the decentralized fuzzy adaptive outputfeedback fault-tolerant control problem for nonlinear switched large-scale systems with sensor faults and unknown control gains, a decentralized fault-tolerant control (FTC) strategy is proposed. As only the actual outputs are measurable when the sensor faults occur, a novel state observer is designed to estimate unmeasured states and address unknown control gains simultaneously. The unknown nonlinear functions are approximated by fuzzy logic systems. Based on the backstepping technique and the average dwell time method, decentralized FTC controllers are designed. It is proven that all states of the closed-loop system are semiglobal uniformly ultimately bounded and the tracking errors can converge to a small neighborhood of zero. A simulation example is presented to show the effectiveness of the developed strategy.

Intelligent Control of Performance Constrained Switched Nonlinear Systems With Random Noises and Its Application: An Event-Driven Approach

In this paper, the adaptive fuzzy control of switched stochastic nonlinear systems with set-time prescribed performance based on event-driven mechanism is studied. The creative part of this paper is that based on the set-time performance function, a modified event-triggered strategy that considers asynchronous switching to deteriorate system performance without strict assumptions is presented, which avoids Zeno behavior and saves communication resources. Then, by using backstepping recursive design technique, It <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\hat {o}$ </tex-math></inline-formula> ’s differential lemma and mode-dependent average dwell time (MDADT) method, a novel adaptive performance control scheme is proposed, which can ensure that all the variables in the system are semiglobally uniformly ultimately bounded (SGUUB) in probability and the tracking error gets into prescribed boundary no later than an arbitrarily adjusted setting time. Finally, the proposed algorithm is applied to a RLC circuit and its practicability is verified via simulation results.

Observer‐based active fault‐tolerant control for a class of pure‐feedback switched nonlinear systems

SummaryAn active fault‐tolerant control (FTC) strategy for a class of switched nonlinear systems in pure‐feedback form by using average dwell time method is investigated in this article. The unknown functions in the system are approximated directly by fuzzy logic systems. A fuzzy state observer is designed to estimate the unavailable states, based on which, a fault detection project is designed. In fault‐free case, all the signals in the closed‐loop system are proved to be bounded under the control of the designed input. The fault estimation and FTC projects will be activated after a fault has been detected. In addition, the active FTC is constructed in the framework of backstepping design technique. The proposed controller guarantee that all the closed‐loop signals remain bounded under a class of switching signals with average dwell time. The simulation results show the effectiveness of the proposed method.

Stochastic stability and stabilization of positive Markov jump linear impulsive systems with time delay

This paper investigates the stochastic stability and stabilization of positive Markov jump linear impulsive systems (PMJLIS) with time delay. First, by choosing appropriate co-positive Lyapunov–Krasovskii functional and using the impulsive average dwell-time method, a stochastic stability criterion is provided for PMJLIS with time delay. Based on this criterion, for PMJLIS with time delay, the stabilization conditions are given using state feedback and impulse feedback, respectively. According to this criteria, the stochastic stability of the systems can be judged and the controllers can be designed only from some relations of the coefficient matrices, Markov jump parameters and delay. To illustrate the main results, a simulation example is provided at the end with a state-feedback controller and an impulsive controller is designed, respectively, which makes the corresponding closed-loop systems be positive, globally asymptotically stable in probability and globally asymptotically stable in mean.

Improved ADT Method for the Switched Nonlinear System: Stability Analysis and Application

This brief investigates the stabilization problem of switched nonlinear systems via orchestrating unstable modes. The stabilizing-switching-dependent average dwell time method is advanced to provide enough switching behaviors with stabilizing property to compensate for the increment of the Lyapunov functions caused by modes and dwell-time-dependent/independent destabilizing switching times. The stability criteria are established based on the set of switching pairs with the stabilizing property. By limiting the ratio of stabilizing switching times in one switching period, the destabilizing switching behaviors allowably occur before the stabilizing ones. Besides, the stability results are applicable for the scenario where the preset switching signals with information loss. Finally, the simulation part illustrates the feasibility and superiority of the obtained results.

Exponential stability of totally positive switched linear systems with both stable and unstable subsystems

AbstractThis article discusses the exponential stability of totally positive switched linear systems (TPSLSs) for continuous‐time and discrete‐time cases. By employing the multiple piecewise‐continuous linear copositive Lyapunov function (MPLCLF) and mode‐dependent average dwell time (MDADT) methods, TPSLSs containing both stable and unstable subsystems are firstly considered and two kinds of switching strategies are proposed, which reduce the conservativeness greatly and provide a more relaxed constraints on parameters compared with the previous results. Finally, two examples are given to illustrate the effectiveness of our results.

Event-triggered control for nonlinear systems involving hybrid impulses

In this paper, we apply event-triggered control to nonlinear systems with impulses, and investigate the problem of ensuring globally exponential stability (GES) of the systems, where events and impulses may occur at different time. Moreover, two types of impulses (i.e., stabilizing and destabilizing) can coexist. On the basis of Lyapunov method and impulsive control theory, some sufficient conditions ensuring GES are derived, and the Zeno behaviour can be excluded. These conditions are presented in the form of linear matrix inequalities (LMI). In particular, inspired by average dwell-time methods, conditions for restriction of impulses are proposed, which guarantee GES of nonlinear systems involving single stabilizing and destabilizing or multiple impulses, respectively. Furthermore, the problem of designing event-triggered mechanism and control gains are solved by using LMI method. Lastly, two numerical simulation examples are given to represent the effectiveness of our results.

Stability analysis for 2‐D switched Takagi‐Sugeno fuzzy systems with stable and unstable subsystems

AbstractThis paper is concerned with the problem of stability of two‐dimensional (2‐D) switched Takagi‐Sugeno (T‐S) fuzzy systems with stable and unstable subsystems described by the Roesser model with constant delays. The T‐S fuzzy model is applied to close the discrete‐time nonlinear subsystems. By utilizing the definitions of mode‐dependent average dwell time (MDADT) method and a quasi‐alternative switching signal, the stability condition for 2‐D discrete‐time switched systems composed of stable and unstable subsystems is derived, and a study on one‐dimentional (1‐D) system can be seen as a special case. Finally, the effectiveness and advantage of the obtained results are illustrated through practical example by LMI toolbox.

Protocol-based control for nonlinear systems with environment-dependent energy harvesting sensors: An average dwell-time method

In this paper, a protocol-based controller is designed for nonlinear systems with multiple sensors, which are powered by environment-dependent energy harvesting (EDEH) devices. The Round–Robin (RR) protocol is adopted to coordinate the data transmission of sensors. The protocol-based transmission can be realized only when the energy harvested by EDEH devices is sufficient. The aim of this paper is to design the protocol-based controller to ensure the stochastic finite-time boundedness with EDEH and RR protocol. Firstly, modeling the EDEH by a switching sequence with varying sojourn probabilities, assuming a finite battery capacity constraint, and associating protocol-based transmission with a given energy cost, we propose a new recursive model to depict the dynamic of energy levels for each sensor. Then, combining with the stochastic analysis method and the dynamic of energy levels, the explicit expressions of the controller for each environment with average dwell time (ADT) are obtained. Finally, an example is provided to demonstrate the effectiveness of the designed controllers.

NN‐based decentralized adaptive event‐triggered control for nonlinear interconnected systems under intermittent DoS and injection attacks

SummaryThis article investigates the problem of decentralized adaptive neural network event‐triggered control of strict feedback nonlinear interconnected systems suffering injection attacks and intermittent denial‐of‐service (DoS) attacks. When DoS attacks occur, the sensor‐controller communication channel is jammed. This may result in system states and traditional backstepping methods are unavailable. A novel switching‐type state observer is constructed to overcome the aforementioned challenges. When the injection attacks occur, the input signals of the controller‐actuator communication channel are changed. A decentralized adaptive event‐triggered controller is designed by using the backstepping method, where a first‐order sliding mode differentiator is introduced to avoid “computational explosion.” The observer gain is derived via the linear matrix inequality technique simultaneously. By using an improved average dwell time method and Lyapunov function theory, all closed‐loop signals are bounded. Finally, a numerical example is used to verify the effectiveness of the proposed control scheme.

Pth moment input-to-state stability of impulsive stochastic functional differential systems with Markovian switching

The paper introduces a unified criterion for pth moment input-to-state stability (p-ISS), pth moment integral input-to-state stability (p-iISS), and eσt-weighted pth moment integral input-to-state stability (eσt-p-ISS) of impulsive stochastic function differential system with Markovian switching under the perturbation of the stabilizing impulse and destabilizing impulse. The Lyapunov function approach, comparison principle, and impulsive average dwell-time method are applied in this paper. The linear coefficients of the upper bound of Lyapunov functional differential operators are time-varying functions, including the case of constants, which advances and improves the existing results. In addition, the same results were obtained by applying impulse differential inequality. At the end of this paper, we use a numerical example to verify the validity of the results.

A new switching law for event-triggered switched systems under DoS attacks

Networked control systems have unique advantages, but it might suffer from attacks, and the resulting asynchronous switching will greatly degrade the system performance and increase the difficulty of controller design. To address this challenge, in this paper, a new switching law and a resilient adaptive event-triggering strategy (RA-ETS) are proposed for networked switched systems to mitigate the negative impacts of asynchronous switching and denial of service (DoS) attacks By utilizing the new switching law, asynchronous switching is converted to expected and unexpected synchronous switchings. According to the minimum DoS sleeping time, the constraints on average dwell time and minimum dwell time are obtained for this switching law, and the sufficient conditions for the existence of expected synchronization are derived. Moreover, RA-ETS is designed to prevent the useless data during attacking from being triggered and to adjust the triggering frequency adaptively if no attacks. Subsequently, the stability of switched systems with an H∞ performance index is ensured by virtue of the average dwell time method and piecewise Lyapunov–Krasovskii functional technique. In particular, the coupling relationship among the DoS attacking, expected and unexpected synchronous intervals is revealed. Finally, the effectiveness of the proposed approach is illustrated by a numerical simulation.

Saturated impulsive control of nonlinear systems with applications

The problem of saturated impulsive control of nonlinear systems is studied, where the saturation structure of impulse action is fully considered. Based on impulsive control theory and average dwell time (ADT) method, sufficient conditions for local exponential stabilization (LES) are derived. An optimization problem on designing controller is presented in order to maximize the domain of attraction. To get a less conservative estimate of the domain of attraction, a linear matrix inequality (LMI) based algorithm is proposed to solve such kind of optimization problems. The applications of the developed results are illustrated through examples from a Chua’s circuit and a problem of pulse transmission of a simple ball motion model.

Finite-time event-triggered filtering of the discrete-time switched linear systems with time delay

The finite-time event-triggered filtering of the discrete-time switched linear systems with time delay is addressed in the paper. The switched system and its filtering switched system are established as a filtering error system (FES) with augmented switching signal by the merging switching signal technique. The asynchronous switching phenomenon of switched system modes and filter modes occurs since a mode-dependent event-triggered transmission scheme (METS) which determines the system output and switching signal is addressed. Meanwhile, by the average dwell time (ADT) and multi-Lyapunov functional method, some sufficient conditions are given to make certain that the FES is finite-time bounded (FTB) and has a specified performance. Furthermore, the finite-time filter is designed by solving linear matrix inequalities. Ultimately, a numerical example is inspired to manifest the availability of the effects in the study.