Persistent Dwell-time Research Articles

$\mathcal {H}_{\infty }$ 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.

Nonfragile H∞ Synchronization of BAM Inertial Neural Networks Subject to Persistent Dwell-Time Switching Regularity.

This article concentrates on the synchronization of discrete-time persistent dwell-time (PDT) switched bidirectional associative memory inertial neural networks with time-varying delays. Through the use of the switched system theory related to the PDT, the convex optimization technique together with some straightforward decoupling methods, an appropriate mode-dependent controller with nonfragility is developed to acclimatize itself to some practical circumstances. Simultaneously, sufficient conditions of ensuring the H∞ performance and exponential stability for the resulting switched synchronization error system are derived. Finally, a numerical example is utilized to show the validity of the model constructed and the influence of the PDT on the H∞ performance. In addition, an image encryption example is employed to show the potential application prospect of the investigated system.

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.

Simultaneous reduced‐order control and fault detection for discrete‐time switched systems with relaxed persistent dwell time regularity

AbstractThis paper focuses on the problem of simultaneous control and fault detection (FD) for discrete‐time switched systems. The main goal is to develop a control/detection unit (CDU) associated with a switching law to control the system and detect faults simultaneously. When the switched systems are with partial measurable states, we directly use these states to construct partial control and FD signals. Next, the reduced‐order CDU is designed to generate the other control and FD signals. Compared with existing results based on full‐order CDU, the proposed results lead to less conservatism and reduce design complexity. The switching law is constructed in the frame of persistent dwell time (PDT) switching. A novel switching number constraint condition is introduced, which further relaxes the restrictions on the dwell time of switching processes of PDT. The less restriction on dwell time degrades the performance requirement of each subsystem and upgrades the degree of freedom for switching law design. Based on the proposed results, a class of nonweighted performance indexes is introduced to characterize the fault sensitivity and robustness. Finally, the effectiveness of the proposed method is illustrated by an example.

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 [formula omitted] filtering for persistent dwell‐time switched piecewise‐affine systems against deception attacks

In this paper, the finite-time l2−l∞ filtering problem is investigated for discrete-time switched piecewise-affine systems against deception attacks, where switching signals are subject to the persistent dwell-time strategy. Considering the effect of deception attacks, a set of random variables obeying the Bernoulli distribution is used to describe the probability of false data injection between the plant and the filter. Based on the partition of state space with different operating regions, the objective of this paper is to design a mode-dependent and region-dependent filter such that the filtering error system is finite-time bounded and satisfies an l2−l∞ performance. By resorting to Lyapunov stability theory and finite-time analysis theory, some sufficient conditions are proposed to obtain such a desired filter. Finally, the availability of the proposed approach is demonstrated by two simulation examples.

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.

Asynchronous Control for Discrete-time Switched Time-delay Systems with Mode-dependent Persistent Dwell-time

Asynchronous Control for Discrete-time Switched Time-delay Systems with Mode-dependent Persistent Dwell-time

Event-triggered adaptive NN control for MIMO switched nonlinear systems with non-ISpS unmodeled dynamics

This paper investigates the problem of event-triggered adaptive neural network (NN) control for multi-input multi-output (MIMO) switched nonlinear systems with output and state constraints and non-input-to-state practically stable (ISpS) unmodeled dynamics. A nonlinear mapping is firstly utilized to deal with output and state constraints. Also, by developing a new switching signal with persistent dwell-time (PDT) and a switching dependent dynamic signal, the difficulty caused by some non-ISpS unmodeled dynamics is overcome. Then, a type of switching event-triggering mechanisms (ETMs) and event-triggered adaptive NN controllers of subsystems are designed, which handle the issue of asynchronous switching without requiring any known restriction on maximum asynchronous time. A piecewise constant introduced into this ETM effectively ensures a strict positive lower bound of inter-event times. Zeno behavior is thus ruled out. Finally, by proposing a novel class of switching signals with reset PDT, it is ensured that all output and state constrains are never violated and all signals of the switched closed-loop system are semi-global uniform ultimate boundedness (SGUUB). A two inverted pendulum system and a numerical example are provided for illustrating the applicability and validity of the proposed method.

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.

Event-triggered sliding mode control for switched genetic regulatory networks with persistent dwell time

This paper focus on the event-triggered sliding mode controller design for discrete-time switched genetic regulatory networks (GRNs) with persistent dwell time (PDT) switching. Firstly, the observation error dynamics of switched GRNs with PDT is constructed in the light of event-triggered sliding mode control (SMC) scheme. Next, sufficient conditions are derived to ensure the exponential stability of the augmented plant. Moreover, an event-triggered SMC law is synthesized to impel the system trajectories onto the sliding surface in a finite time. Finally, a verification example is provided to illustrate the effectiveness and potential of the proposed method.

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.

Fault-Tolerant $${H_\infty }$$ Control for T–S Fuzzy Persistent Dwell-time Switched Singularly Perturbed Systems with Time-Varying Delays

Fault-Tolerant $${H_\infty }$$ Control for T–S Fuzzy Persistent Dwell-time Switched Singularly Perturbed Systems with Time-Varying Delays