Average Dwell Time Switching Signals Research Articles

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.

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.

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.

Unified stability criteria of asynchronous discrete-time impulsive switched delayed systems: bounded admissible edge-dependent average dwell time method

This article investigates input-to-state stability (ISS) problem of asynchronous discrete-time impulsive switched delayed systems, in which switching and impulse may be asynchronous. A novel bounded admissible edge-dependent average dwell time (BAED-ADT) switching signal is designed. Based on this division rule of switching subsystems, we adopt the slow switching method for the stable subsystems and the fast switching method for the unstable subsystems, so that stable subsystems can compensate unstable subsystems. Combined with admissible edge-dependent average impulsive interval (AED-AII) impulsive signal, a new unified ISS stability result is established, which could be applied to impulsive switched systems with an arbitrary combination of unstable and stable subsystems. Without solving the linear matrix inequality, it is allowed to readjust the AED-ADT boundary of the newly proposed stability condition according to the actual impulsive and switching signal. Further, compared with the existing fruits, the new stability condition is an extension and improvement of the previous one, which is less conservative. Several numerical examples are provided to show the validity of the conditions and the advantages of the theoretic results.

Finite-time H∞ control for switched fuzzy systems: A dynamic adaptive event-triggered control approach

This paper investigates the finite-time H∞ control problem for switched fuzzy systems using the edge-dependent average dwell time switching. A dynamic event-triggered mechanism is adopted to alleviate communication pressure. An adaptive law is set up to adjust the threshold on-line, which deeply affects the triggering times. It is rigorously proved that the Zeno behavior is excluded. A set of dynamic event-triggered controllers and edge-dependent average dwell time switching signals are co-designed to achieve desired performance. Finally, a chemical reaction example is given to validate the effectiveness of the proposed method.

Stabilization of discrete-time positive switched T-S fuzzy systems subject to actuator saturation

<abstract><p>The stabilization of discrete-time positive switched Takagi-Sugeno (T-S) fuzzy systems with actuator saturation is investigated in this paper. It is assumed that the switched subsystems are partially stabilizable. Based on the convex hull technique (CHT) and parallel distribution compensation (PDC) algorithm, a saturated fuzzy controller and slow-fast combined mode-dependent average dwell time (MDADT) switching signal are co-designed and sufficient conditions for the positivity and stability of closed-loop positive switched T-S fuzzy systems (PSTSFSs) are developed, which can be reduced to the ones under the case where all switched subsystems are stabilizable. Moreover, the largest attraction domain estimation (ADE) is given for PSTSFSs by formulating an optimization problem. Finally, the designed control scheme is applied to two illustrative examples to verify its availability and superiority.</p></abstract>

Stability and Stabilization of Polynomial Fuzzy-Model-Based Switched Nonlinear Systems Under MDADT Switching Signal

This article proposes a novel Lyapunov stability analysis for a class of switched nonlinear systems under the mode-dependent average dwell time (MDADT) switching signals. For the first time, a polynomial fuzzy model is used to describe the nonlinearity of the switched systems instead of a Takagi–Sugeno fuzzy model, which can represent a wider range of nonlinear plants. As existing advanced results are relatively conservative and lead to that tighter bounds on the dwell time are not easy to be obtained, therefore, the stability analysis for switched systems is still quite challenging. In this article, to tackle this problem, by developing a polynomial multiple Lyapunov function (MLF) approach and exploring the feature of the membership functions, relaxed stability conditions are derived for the switched polynomial fuzzy-model-based control systems. In particular, the polynomial MLF is guaranteed radially unbounded by a two-step procedure, making traditional quadratic MLF a specific case, thereby improved stability conditions can be established in the form of sum-of-squares. Moreover, the new algorithm for multivariate Chebyshev membership functions based on linear programming is proposed to introduce the information of membership functions and further relax the stability conditions to obtain tighter bounds on MDADT. Finally, a simulation example demonstrates the effectiveness of the developed techniques.

Event‐triggered H∞ control of discrete‐time switched linear systems with delays

AbstractThis paper studies the control problem of discrete‐time delayed switched systems with average dwell time switching signals using event‐triggered mechanism. The event‐triggered mechanism can reduce redundant information transmission. First, employing state‐feedback controller, two sufficient conditions are proposed to guaranteeing (i) exponential stability of the disturbance‐free closed‐loop system and (ii) performance of the closed‐loop system with disturbance. Moreover, the controller gain is explicitly computed by solving a set of linear matrix inequalities. Second, results obtained for state‐feedback controller are extended to those for observer‐based state‐feedback controller, and both the controller and observer gains are explicitly computed. All conditions are derived by utilizing a properly constructed decay‐rate‐dependent Lyapunov functional. Finally, a numerical example illustrates the validity of the obtained theoretical results.

Stochastic input-to-state stability for nonlinear impulsive switched systems with random impulses coupled by multiple jump maps

This article focuses on a class of nonlinear random impulsive and switched systems for stochastic input-to-state stability. The impulse is divided into two types: single jump map and multiple jump maps. When the impulse is chosen as single jump map, it means that the impulse between the two adjacent switching times is single as well as impulse and switching occur simultaneously, in which the impulsive moments are fixed. When the impulse is chosen as multiple jump maps, in this model, the impulse is not only limited by multiple maps, but also the impulse instants are assumed to be random. Therefore, this model is an extension of the traditional impulsive and switched system. In view of admissible edge-dependent average dwell time switching signal and the impulse dynamic satisfying Poisson’s process, sufficient conditions for the stochastic input-to-state stability are introduced into nonlinear impulsive switched system with random impulses. Three significant distinctions from the existing results rest with that (1) a new multiple Lyapunov functions are first created; the novelty contains discontinuity at the discrete points including switching moments and the impulse jump instants of Lyapunov-like functional; (2) the coefficient of derivative of a Lyapunov-like functions is permitted to be either positive or negative, which is less conservative; (3) the adopted admissible edge-dependent average dwell time switching scheme delves into less conservative stochastic input-to-state stability condition than mode-dependent average dwell time switching, nonlinear impulsive switched system with various jump maps. Numerical examples are simulated to manifest the validity of the main results.

Stability analysis for nonlinear switched singular systems via T-S fuzzy modeling

The stability for discrete nonlinear switched singular systems with unstable subsystems is investigated. First, by constructing an appropriate multiple discontinuous Lyapunov function, and utilizing the characteristics of mode-dependent average dwell time switching signals, new stability results for nonlinear switched singular system are established. Then, we adopt the T-S fuzzy modeling method to approximate the nonlinear switched singular systems and get general stability conditions in forms of linear matrix inequalities. Compared to the current results, our technique is more flexible and we also get tighter dwell time boundaries. Furthermore, a numerical example demonstrates the effectiveness of the proposed method.

Finite-time and sampled-data synchronization of complex dynamical networks subject to average dwell-time switching signal

This study deals with the finite-time synchronization problem of a class of switched complex dynamical networks (CDNs) with distributed coupling delays via sampled-data control. First, the dynamical model is studied with coupling delays in more detail. The sampling system is then converted to a continuous time-delay system using an input delay technique. We obtain some unique and less conservative criteria on exponential stability using the Lyapunov–Krasovskii functional (LKF), which is generated with a Kronecker product, linear matrix inequalities (LMIs), and integral inequality. Furthermore, some sufficient criteria are derived by an average dwell-time method and determine the finite-time boundedness of CDNs with switching signal. The proposed sufficient conditions can be represented in the form of LMIs. Finally, numerical examples are given to show that the suggested strategy is feasible.

Polynomial stability of positive switching homogeneous systems with different degrees

In this article the polynomial stability for positive switching homogeneous systems with different degrees is investigated by proposing a logarithm contraction average dwell-time method. By introducing a class of logarithm contraction average dwell-time switching signals and a piecewise maximum Lyapunov function, we establish an explicit criterion for global polynomial stability of positive switching homogeneous systems whose degrees are greater than one. Especially, the main result is applicable to polynomial stability of Persidskii-type switching systems and consensus of multi-agent systems.

Multiple event‐triggered schemes for a class of switched descriptor systems with asynchronous switching

AbstractThis article studies asynchronous switching for a class of switched descriptor systems (SDSs) under multiple event‐triggered schemes (ETSs). First, by using a mode‐dependent coordinates transformation, a SDS is equivalently transformed into a reduced‐order ordinary switched linear system with state jumps. Then, multiple ETSs are used to transmit the state and switching signal information. The asynchronism between system modes and controller modes inevitably happens in a switching interval. Next, by constructing a controller‐mode‐dependent Lyapunov functional and using the asynchronous switching strategy, an exponential stability criterion is presented for the closed‐loop system with average dwell time switching signals. Meanwhile, the state feedback controller and multiple ETSs are codesigned. Besides, the Zeno behavior is avoided. In the end, the validity of the proposed method is demonstrated by a numerical example.

Observer-Based Adaptive Neural Output Feedback Constraint Controller Design for Switched Systems Under Average Dwell Time

Aiming at a class of switched uncertain nonlinear strict-feedback systems under the action of average dwell time switching signal, this paper proposes a novel adaptive neural network output feedback tracking control based on the consideration of the full state constraints. The controller is proposed based on neural networks. One of the key characteristics of the system discussed is that the state variables cannot be measured and the system states need to be kept within the constraint ranges. For the sake of estimating the unmeasured states, the observer is constructed. In order to ensure all states which are within the time-varying boundary, the tangent barrier Lyapunov function (BLF-Tan) is selected in the design process. The boundedness of the closed-loop signals with average dwell time is guaranteed by the designed controllers and all the states limit in their constrained sets. It has been proved that the output tracking error converge to a small neighborhood of zero. In addition, the significance of the presented control strategy is verified and tested by a simulation example.

Annular finite-time [formula omitted] control of switched fuzzy systems: A switching dynamic event-triggered control approach

This paper addresses the annular finite-time boundedness H∞ control problem for a class of switched fuzzy systems. A novel switching dynamic event-triggered mechanism is proposed to save communication resources; where two different internal variables are designed and change according to a switching manifold. It is proved that the proposed switching dynamic event-triggered mechanism has a larger minimal inter-execution time in comparison with the static one. With a Lyapunov-like function including the internal dynamic variable, a criterion is established to ensure the annular finite-time boundedness H∞ performance. A dynamic event-triggered controller and a set of feasible mode-dependent average dwell time switching signals are co-designed to achieve desired performance. Finally, an example is presented to validate the effectiveness of the proposed method.

Finite-time stabilization of continuous-time switched positive delayed systems

This paper deals with the problems of finite-time stability and stabilization for continuous-time switched positive linear time-delay systems under mode-dependent average dwell time switching signals. First, finite-time stability conditions are established by constructing an multiple piecewise copositive Lyapunov–Krasovskii functional. Then, finite-time stabilization is achieved by designing a state-feedback controller in the form of linear programming. This numerical construction approach proposed for controller cancels the restriction of the multiple piecewise copositive Lyapunov–Krasovskii functional on controllers, which can decrease the conservatism. Finally, two numerical examples are given to show the advantages of our methods.

Stochastic finite-time stabilization for discrete-time positive Markov jump time-delay systems

In this paper, the problems of stochastic finite-time stability and stabilization of discrete-time positive Markov jump systems are investigated. To deal with time-varying delays and switching transition probability (STP), stochastic finite-time stability conditions are established under mode-dependent average dwell time (MDADT) switching signal by developing a stochastic copositive Lyapunov-Krasovskii functional approach. Then a dual-mode dependent output feedback controller is designed, thus stochastic finite-time stabilization is achieved based on linear programming technique. Finally, two examples are given to show the effectiveness of our results.

Stabilization of Enforced Positive Switched Linear Systems with Bounded Controls

This paper is concerned with the controller synthesis issue for enforced positive switched linear systems via output feedback. First, the stabilization problem is studied with output feedback under average dwell time switching signal, and the controllers we proposed guarantee stability and positivity of the closed-loop systems. Second, the output feedback stabilization issue is investigated by introducing special form of diagonal matrices, and the constraints on states and control inputs are solved based on limited initial conditions. Then, the derived conditions are described via linear programming, also extending the theoretical findings to constrained output issue. Finally, the simulation results demonstrate the feasibility of the control strategy.

Asynchronous l 2 – l ∞ filtering of discrete-time impulsive switched systems with admissible edge-dependent average dwell time switching signal

In this paper, the asynchronous filtering problem is directed at a kind of discrete-time impulsive switched systems, where ‘asynchronous’ implies that there is a delay when switching occurs between filter modes and system modes. A novel Lyapunov function has been constructed. The inventiveness lies in discontinuity of Lyapunov-like function at both the switching time and the instant when the system modes and filter modes are matched. An improved inequality portraying the relationship among Lyapunov-like function, impulse, asynchronous phenomena and disturbance is built to pledge the performance. On the basis of directed graph, the novel Lyapunov function, the improved inequality and admissible edge-dependent average dwell time technology, some criteria suitable for proving the globally uniformly exponential stability of filtering error system are proposed with performance index, and the relevant filter can also be designed. Finally, three numerical examples show the availability of the obtained conclusions.

Actuator and sensor fault estimation for discrete-time switched T–S fuzzy systems with time delay

In this paper, actuator and sensor fault estimation is investigated for switched Takagi–Sugeno (T–S) fuzzy systems with time delay. The purpose is to complete research on fault diagnosis in these systems by switching the degree of membership of the T–S fuzzy system. First, the nonlinear time-delay switched system is described as a T–S fuzzy switched model. Then, based on the average dwell-time (ADT) switching signal and the Lyapunov function technique, a fuzzy-parameter-dependent observer is designed for estimating the actuator and sensor faults simultaneously. This method can guarantee that the error system is globally, uniformly, and asymptotically stable (GUAS) with a measurable H∞ performance index. Finally, simulation results are presented to demonstrate the effectiveness of the proposed technique.