Persistent Dwell-time Switching Research Articles

Fuzzy $\mathcal {H}_{\infty }$ Sliding Mode Control of Persistent Dwell-Time Switched Nonlinear Systems

In this article, the fuzzy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> sliding mode control problem for continuous-time switched nonlinear systems is investigated. The switching signal conforms to the persistent dwell-time switching mechanism. The first objective of this article is to construct a switched integral sliding surface that not only accommodates the switched nonlinear model, but ensures that the sliding mode dynamics are globally uniformly exponentially stable and have an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance by the equivalent controller derived from the sliding surface. Another aim is to integrate the switched sliding mode control law to force the system trajectories to the sliding surface in a finite amount of time. Then, on the basis of the Lyapunov function technique, the specific form of the sliding mode control law gains is given first, and later the finite-time reachability of the sliding surface is ensured. Finally, the validity of the proposed switched sliding mode control method is validated by a numerical example.

Mixed [formula omitted]/passive synchronization for persistent dwell-time switched neural networks via an activation function dividing method

The mixed H∞/passive synchronization issue of discrete-time switched neural networks is studied in this paper. In order to regulate the switching between subsystems, the persistent dwell-time switching law is adopted. The paper aims to design a suitable synchronization controller to make the synchronization error system satisfy the mixed H∞/passive performance and achieve global uniform exponential stability. By employing Lyapunov stability theory, performance analysis criteria and the synchronization controller design method are given, in which an activation function dividing method is employed to reduce their conservatism. Simulation results demonstrate the superiority and effectiveness of the method.

$\mathcal {H}_{\infty }$ Fuzzy Dynamic Output Feedback Reliable Control for Markov Jump Nonlinear Systems With PDT Switched Transition Probabilities and Its Application

This article investigates the problem of designing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> dynamic output feedback reliable controller for discrete-time Markov jump nonlinear systems with persistent dwell-time switched transition probabilities based on the Tagaki–Sugeno fuzzy model. The uncertainty of measurement output, which is assumed to occur randomly, and mode-dependent actuator faults are considered simultaneously. Moreover, the jumping property presented by system modes is described by the Markov chain of which transition probabilities are considered to be piecewise time-varying, and is described by adopting the more flexible persistent dwell-time switching rule. Based on the stochastic analysis approach and Lyapunov stability theory, some sufficient conditions are established to ensure the resulting closed-loop system being mean-square exponentially stable with the prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance. Furthermore, the desired controller gains can be obtained through solving a convex optimization problem. Finally, the practicability and availability of the proposed control method are illustrated by a numerical example and a modified tunnel diode circuit model.

Quantized Interval Type-2 Fuzzy Control for Persistent Dwell-Time Switched Nonlinear Systems With Singular Perturbations.

This article investigates the problem of quantized fuzzy control for discrete-time switched nonlinear singularly perturbed systems, where the singularly perturbed parameter (SPP) is employed to represent the degree of separation between the fast and slow states. Taking a full account of features in such switched nonlinear systems, the persistent dwell-time switching rule, the technique of singular perturbation and the interval type-2 Takagi-Sugeno fuzzy model are introduced. Then, by means of constructing SPP-dependent multiple Lyapunov-like functions, some sufficient conditions with the ability to ensure the stability and an expected H∞ performance of the closed-loop system are deduced. Afterward, through solving a convex optimization problem, the gains of the controller are obtained. Finally, the correctness of the proposed method and the effectiveness of the designed controller are demonstrated by an explained example.

Semi-time-dependent stabilization for a class of continuous-time impulsive switched linear systems

In this paper, the stability and stabilization problems of a class of impulsive switched linear systems with mode-dependent persistent dwell-time (MPDT) switching are investigated in continuous-time domain. The proposed switching law is more general, which not only covers the widely probed dwell-time (DT) and average dwell-time (ADT) as special cases but also extends the persistent dwell time (PDT) in the literature. By invoking novel modal partition time-dependent multiple Lyapunov-like functions, the stability criteria for the systems under MPDT switching in nonlinear settings are established as a first attempt, upon which the desired mode-dependent and semi-time-dependent (STD) stabilizing controllers for continuous-time impulsive switched linear systems are designed. It is demonstrated that the control performance is improved as both the length of admissible MPDT and the number of time partition segment are added. Finally, a numerical example is provided to illustrate the potential of the obtained theoretical results.

H ∞ State Estimation for Switched Inertial Neural Networks With Time-Varying Delays: A Persistent Dwell-Time Scheme

The <inline-formula> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> state estimation issue for switched delayed inertial neural networks is addressed in this work. A more universal switching law, persistent dwell-time (DT) switching law, is considered here rather than average DT one of which switching frequency among subsystems is strictly limited, or DT one. Concurrently, time delays are inevitable when transmitting information, then taking the time-varying delays into account makes the constructed systems conform well with the actual situations. The main goal in the work is devoted to designing a state estimator to ensure that the state estimation error system is globally uniformly exponentially stable and satisfies a prescribed <inline-formula> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> noise attenuation level. A mixed time/mode-dependent Lyapunov&#x2013;Krasovskii functional matched with the foregoing switching law is introduced. Through utilizing some reasonable inequalities and common matrix operations, some sufficient criteria which guarantee the aforesaid stability and the solvability of the addressed issue are presented. Finally, an illustrative example is provided to present the potentiality and validity of the developed results.

Finite-time bounded control for quadrotors with extended dissipative performance using a switched system approach

In order to deal with the problem of attitude tracking control for quadrotors subject to time-varying inertia and external disturbances, a finite-time bounded switched linear parameter-varying (LPV) control method is presented. The attitude dynamics is described by two subsystems, where the inner angular-velocity system is used to track the desired angular velocities that are generated by the outer attitude-angle system. The angular-velocity system of quadrotors is modeled as a switched LPV model, where a family of linear models is developed to approximate the original nonlinear system and the LPV method is applied to model the time-varying inertia. Specially, a mode-dependent persistent dwell-time (MPDT) switching logic, which is more general than the typically used dwell-time (DT) or average dwell-time (ADT) switching logic, is adopted to govern the switching behaviors among these linear models. A state-feedback controller for the switched LPV error-tracking system is designed, which ensures both finite-time boundedness and extended dissipative performance. Finally, the developed theoretical results are verified by numerical simulation.

Fuzzy multi-objective fault-tolerant control for nonlinear Markov jump singularly perturbed systems with persistent dwell-time switched transition probabilities

This paper studies the discrete-time slow state feedback fault-tolerant controller design issue for Takagi-Sugeno fuzzy-model-based Markov jump singularly perturbed nonlinear systems, in which transition probabilities of systems subject to persistent dwell-time switching mechanism. In order to eliminate the influence of actuator faults and provide a more flexible control strategy, a multi-objective fault-tolerant controller is designed to ensure the stability of the system and meet the requirements of various performance indexes. The goal is to establish some sufficient conditions, which ensure the mean-square exponential stability and the extended dissipativity performance of the closed-loop system. Furthermore, the gains of the designed controller can be obtained by solving the problem of convex optimization. Finally, the availability of the designed controller is demonstrated by a numerical example and a tunnel diode circuit system.

Reliable output feedback control for persistent dwell-time switched piecewise-affine systems against deception attacks

In this paper, the reliable output feedback control issue for discrete-time switched piecewise-affine systems against deception attacks is investigated. The mode of the constructed system is controlled by the persistent dwell-time switching mechanism and the occurrence of deception attacks is assumed to obey Bernoulli distribution. Based on the mode-dependent Lyapunov function and S-procedure theories, for the piecewise-affine systems, a reliable output feedback controller is designed. Some sufficient conditions are established to make sure the underlying systems are mean-square exponentially stable with prescribed H∞ performance. Lastly, the correctness of the derived results is proved via a simulation example.

Non‐fragile dynamic output‐feedback control for ‐gain performance of positive FM‐II model with PDT switching: An event‐triggered mechanism

AbstractIn this article, the design problem of event‐triggered (E‐T) non‐fragile dynamic output‐feedback controller is addressed for the uncertain Fornasini‐Marchesini second (FM‐II) model with persistent dwell time (PDT) switching constraint. First of all, a novel E‐T scheme is introduced to reduce the measurement transmission ratio so as to decrease the occupancy of the communication channels. Then, by choosing a suitable co‐positive type Lyapunov function and utilizing the PDT method, sufficient conditions are obtained under which the obtained closed‐loop system is positive, robustly exponentially stable and has an ‐gain performance. The corresponding controller design issues are simultaneously discussed, and the parameterized matrices are explicitly designed by solving some linear programming inequalities. Finally, a simulation example is provided to show feasibility of the developed theoretical results.

Adaptive sliding mode control for persistent dwell-time switched nonlinear systems with matched/mismatched uncertainties and its application

In this paper, the adaptive sliding mode control issue for switched nonlinear systems with matched and mismatched uncertainties is addressed, where the persistent dwell-time switching rule is introduced to describe the switching of parameters. Besides, considering the case that the upper bound of the matched uncertainty is unknown, the purpose of this paper is to utilize an adaptive control method to estimate its upper bound parameters. To begin with, a linear sliding surface is constructed, and then the reduced-order sliding mode dynamics can be obtained through a reduced-order method. Next, sufficient conditions can be derived based on the Lyapunov stability and the persistent dwell-time switching analysis techniques ensuring that the reduced-order sliding mode dynamics is globally uniformly exponentially stable. Moreover, a switched adaptive sliding mode control law is designed, which can not only ensure the reachability of the sliding surface but also estimate the upper bound parameters of the matched uncertainty. Finally, a numerical example and a circuit model are introduced to verify the effectiveness of the proposed method.

New results on stability and L1-gain characterization for switched positive systems: A persistent dwell time approach

This paper is concerned with the problem of stability and L1-gain characterization for a class of switched positive systems consisting of both stable and unstable subsystems. Such systems can be modeled ingeniously as switched positive systems satisfying persistent dwell time switching. Compared to the widely used dwell time and average dwell time switching in the previous literature, persistent dwell time switching is more general due to its covering such two switchings as special cases. A new sufficient criterion ensuring the stability of switched positive systems is derived by using a persistent dwell time approach. And then an unweighted L1-gain is computed by solving a linear programming problem. The presented method in this paper may decrease the conservatism. Finally, the effectiveness and advantage of the provided method are illustrated with an example.

Observer-based [formula omitted] control for persistent dwell-time switched networked nonlinear systems under packet dropout

This paper focuses on the observer-based controller design issue for a class of discrete-time networked nonlinear systems. Due to the stochastic effects, the switching between subsystems occurs. The persistent dwell-time switching mechanism, which is more general than dwell-time switching and average dwell-time switching mechanisms, can well describe these switching cases with both fast and slow switchings. Furthermore, there is packet dropout during data transmission, which is described by Bernoulli white sequence, and a corresponding mechanism is used to compensate for the impact of packet dropout. Then based on the Lyapunov function approach, some sufficient conditions for mean-square exponentially stable and an expected H∞ performance are derived. Finally, an illustrative example that demonstrates the superiority and feasibility of the proposed method is given.

Formula omitted] sliding mode control for PDT-switched nonlinear systems under the dynamic event-triggered mechanism

In this paper, the H∞ sliding mode control problem of persistent dwell-time switched nonlinear systems is investigated. Due to the limited bandwidth resources, a dynamic event-triggered mechanism is introduced to alleviate the transmission burden. Considering that the system parameters are switched in accordance with the persistent dwell-time switching strategy, a novel switched sliding mode control law is constructed. Then, drawing on the Lyapunov function approach, sufficient conditions are derived, which not only ensure the reachability of the sliding region around the specified sliding surface but also guarantee the globally uniform exponential stability of the system with an H∞ performance. Moreover, the specific form of the controller gains is derived by utilizing an efficient decoupling method. Eventually, the validity of the proposed method is validated by two numerical examples.

Simultaneous fault detection and control for discrete-time switched systems under relaxed persistent dwell time switching

This paper investigates the problem of robust control and fault detection for discrete-time switched systems. The main goals are to design controller/fault detectors and a switching rule to guarantee the control and detection objectives simultaneously. The switching rule is constructed based on persistent dwell time (PDT) with an average dwell time (ADT) constraint. The introduced ADT constraint can allow a much smaller PDT lower bound to be designed, which provides more freedom of designing switching signal. Next, some time-varying dynamic output feedback controllers/detectors matching different switching processes of PDT are constructed such that the closed-loop systems meet the desired objectives. The corresponding robust control and fault detection levels can be characterized by a class of non-weighted performance indexes. Finally, the effectiveness of the proposed results is illustrated by an example.

Finite-time energy-to-peak fuzzy filtering for persistent dwell-time switched nonlinear systems with unreliable links

This work investigates the finite-time filtering problem of discrete-time switched nonlinear systems with unreliable links, where the persistent dwell-time switching mechanism is introduced to describe the changes of system mode and the fuzzy set theory is adopted to construct the model of nonlinear systems. Moreover, unreliable links including random nonlinearity and disturbance are employed to transmit data between the plant and the filter. The main intention of this study is to develop a desired full-order filter such that the resulting filtering error system is finite-time bounded with a fixed energy-to-peak performance index. Afterwards, based on the finite-time bounded theory, and through constructing appropriate Lyapunov–Krasovskii functionals, sufficient conditions for the stability with corresponding performance of the filtering error system are established. Then, by solving a set of convex optimization problems, the specific gains of the desired filter are computed. Finally, a numerical example and a single link robot arm model are provided to expound the correctness and practicability of the proposed approach.

Extended dissipative filtering for singularly perturbed systems with random uncertain measurement: A double-layer switching mechanism

This article concentrates on the extended dissipative filtering for slow sampling singularly perturbed systems based on the double-layer switching mechanism containing the Markov jump signal and the persistent dwell-time switching signal simultaneously. The Markov jumping signal, as the upper layer switching signal, is utilized to describe the jumping of system modes. Then, the persistent dwell-time switching signal is introduced as a lower layer switching signal to characterize the variation for transition probabilities of the Markov chain. Besides, the uncertainties of actual measurement output are assumed to randomly occur, which are described by a set of Bernoulli distributed white sequences. Furthermore, some sufficient conditions ensuring the filtering error system being mean-square exponentially stable with an extended dissipative performance are obtained through the Lyapunov stability theory and some advanced linear matrix transformation techniques. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method.

Network-based quantized [formula omitted] control for T–S fuzzy singularly perturbed systems with persistent dwell-time switching mechanism and packet dropouts

This paper focuses on the H∞ control problem for a class of discrete-time persistent dwell-time (PDT) switched nonlinear singularly perturbed systems (SPSs) under T–S fuzzy model. In order to make the system more consistent with the actual situation, the signal quantization associated with a logarithmic quantizer and the packet dropouts governed by a Bernoulli variable are considered simultaneously. And, the persistent dwell-time switching mechanism is employed to describe the fast and slow switching among several subsystems in the investigated systems alternatively. Based on the Lyapunov function approach and Takagi–Sugeno (T–S) fuzzy technique, some sufficient conditions are obtained, which can ensure the exponentially mean-square stable (EMSS) and H∞ performance of the closed-loop system. In addition, a unified fuzzy controller design methodology is established for the nonlinear SPSs, so that the fuzzy controller can be designed depending on whether the fast states of the systems are available or not. Finally, a numerical example and a series DC motor model are provided to demonstrate the superiority and practicability of the obtained theoretical results.

Asynchronous non-fragile control for persistent dwell-time switched singularly perturbed systems with strict dissipativity

This paper focuses on the problem of asynchronous non-fragile dissipativity control for a class of switched singularly perturbed systems (SPSs) governed by the persistent dwell-time (PDT) switching mechanism in the discrete-time context. Unlike some previous results, the modes of system and controller in this paper are assumed to be asynchronized, which conforms better with the practical scenarios. Besides, considering the case that the controllers may be affected by uncertain factors and can not be realized accurately during system operation, the non-fragile mechanism is introduced in the process of controller design to enhance the reliability and security of the SPSs. Based on Lyapunov stability theory and stochastic analysis theory, some sufficient conditions are obtained, which can ensure the exponentially mean-square stable (EMSS) and strict dissipative performance of the closed-loop system. Furthermore, the asynchronous non-fragile slow state variables feedback (SSVF) controller gains are obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example and an inverted pendulum model are applied to demonstrate the superiority and the practicability of the developed control mechanism.

Event-triggered non-fragile control for uncertain positive Roesser model with PDT switching mechanism

In this paper, the issue of non-fragile control is addressed for the positive discrete-time Roesser model with uncertain parameters, where the switching mechanism obeys the persistent dwell time (PDT) constraint. First of all, in order to reduce the resource occupancy, a event-triggered (E-T) mechanism is introduced for the considered positive Roesser model. Then two kinds of non-fragile controllers combining with the E-T scheme are designed. By utilizing the PDT idea and the co-positive-type Lyapunov function method, sufficient conditions to ensure that the resulting closed-loop systems are positive and robust exponentially stable are presented. In addition, explicit expressions for the related controller gain matrices are also provided. Finally, an illustrative simulation example is given to show feasibility of the developed theoretical results.