Switched State Feedback Controller Research Articles

H∞ control of switched Lurie systems with dwell time

This article deals with the [Formula: see text] control problems of switched Lurie systems. Our purpose is to design switching signals and state feedback controllers with time-varying control gains that make the closed-loop switched Lurie systems absolutely stable. Based on switched time-varying Lyapunov–Lurie function, time-varying controllers corresponding to two kinds of switching signals are proposed. On this basis, the control synthesis conditions are given. It is worth mentioning that our results can deal with the situation that all subsystems are not stabilizable. Finally, the obtained results are applied to a flexible joint robotic arm model with switchings of parameter values. Another simulation example of switched Lurie systems is considered to illustrate the validity of the presented approaches.

H∞$$ {H}_{\infty } $$ bumpless transfer control of switched systems with time‐varying delays

AbstractThis paper investigates the bumpless transfer control (HBTC) problem of switched systems with time‐varying delays. A novel smooth switching state feedback controller is designed to eliminate the bumps existing in the classical switched state feedback control strategy. By the use of average dwell time (ADT) and multiple Lyapunov–Krasovskii functionals, some solvability conditions for the HBTC problem are derived. The control gain matrices can be calculated by solving linear matrix inequalities(LMIs). A numerical example is employed to show the validity of the proposed results.

Adaptive event-triggered control for semi-Markovian switching linear systems with process time-varying delays

This paper investigates an adaptive event-triggered control for semi-Markovian jump linear systems with process time-varying delays. For reducing the data transmission amount from the sensor-to-controller, a switching-mode dependent adaptive event-trigger (AET) is proposed wherein a positive auxiliary function is involved. Utilizing the received non-periodical state information, a switching state feedback control law is investigated. By aid of an exponential inequality technique, the controller design method is conveniently presented. The proposed control method not only guarantees the globally exponentially stability of the closed-loop system but also is capable of regulating the decay rate. An approximation approach for the minimal event-triggered time-interval of the AET is given as well. It has been proved that the unwanted Zeno behavior will not exhibit. The proposed control method is employed to a transmission control protocol based active queue management (TCP/AQM) system and the numerical experiment demonstrates its effectiveness.

Design of switching state-feedback controllers for linear systems subject to asymmetric saturations*

This paper considers the problem of controlling a linear system affected by asymmetrical input saturation. The proposed solution is based on using a linear matrix inequality (LMI)-based methodology to find the gains of a switching state-feedback controller. The main difference and contribution when compared to existing approaches is that the switching rule is chosen based on the closed-loop performance that each of the non-saturating controller gains can achieve when used with the current value of the state vector. Although the main focus of the paper is on time-invariant systems, the possible extension to linear parameter-varying (LPV) systems is discussed. An illustrative example is used to show the main features of the proposed approach.

Resilient control design for networked DC microgrids under time-constrained DoS attacks

This paper studies the resilient current controller design for the networked DC microgrid system with multiple constant power loads (CPLs) under a new type of time-constrained denial-of-service (DoS) attack. Different from the existing DoS attack models, which are often characterized by DoS frequency and DoS duration, this paper only considers the duration characteristics of the sporadic/aperiodic DoS attacks, and proposes a new type of time-constrained DoS attack model. Under the effects of such DoS attacks, a switching state feedback control law is constructed and a switching-like DC microgrid system model is then established. Furthermore, based on an attack-parameter-dependent time-varying Lyapunov function (TVLF) method, the exponential stability criterion of the resulting DC microgrid system under aperiodic DoS attacks is derived, and a new resilient controller design method is proposed. Finally, simulation studies are given to verify the effectiveness and merits of the proposed resilient control design scheme on achieving the desired control performance and attack resilience.

An improved finite-time stabilization of discontinuous non-autonomous IT2 T-S fuzzy interconnected complex-valued systems: A fuzzy switching state-feedback control method

<abstract><p>Based on the type-2 Takagi-Sugeno (IT2 T-S) fuzzy theory, a non-autonomous fuzzy complex-valued dynamical system with discontinuous interconnection function is formulated. Under the framework of Filippov, the finite-time stabilization (FTS) problem is investigated by using an indefinite-derivative Lyapunov function method, where the derivative of the constructed Lyapunov function is allowed to be positive. By designing a fuzzy switching state feedback controller involving time-varying control gain parameters, several sufficient criteria are established to determine the considered system's stability in finite time. Correspondingly, due to the time-varying system parameters and the designed time-dependent control gain coefficients, a more flexible settling time (ST) is estimated. Finally, an example is presented to confirm the proposed methodology.</p></abstract>

Finite-time Stabilization of Switched Positive Systems with Time-varying Delays and Actuator Saturation

In this paper, the finite-time stabilization for a class of switched positive systems with time-varying delays and actuator saturation under average dwell time switching is investigated. Through multiple copositive Lyapunov-Krasovskii functionals method, the sufficient conditions for finite-time bounded of continuous-time case are given, and the appropriate switching rules and state feedback controllers are presented together. Moreover, the convex hull technique is employed to deal with actuator saturation. Finally, an illustrative example is given to show the effectiveness of the proposed method.

Finite-time stabilization of high-order output-constrained switched systems via state feedback

In this paper, finite-time stabilization of high-order switched systems with output constraints via state feedback control laws is investigated. Incorporating a common tangent-type barrier Lyapunov function, state feedback controllers are presented in a systematic way by revamping the adding a power integrator approach. With the designed state feedback controllers, switched systems are finite-time stabilized and the output constraint is also guaranteed at the same time. The method is proposed in a unified frame because that it can handle finite-time stabilization problem of high-order switched systems with/without output constraints both, no need of changing switched state feedback controllers’ structure.

Periodicity and global exponential periodic synchronization of delayed neural networks with discontinuous activations and impulsive perturbations

In this paper, periodic dynamics and periodic synchronization of a class of delayed neural networks with discontinuous neuron activations and impulsive perturbations are investigated. Firstly, based on Filippov’s functional differential inclusion and impulsive differential inclusions theory, the existence of solutions of the considered neural network system is studied. Secondly, according to Krasnoselskii’s fixed point theorem on cones of set-valued analysis, sufficient conditions are provided for the existence of at least one periodic solution and at least two periodic solutions for the neural network systems. Furthermore, we also use Kakutani’s fixed point theorem to give sufficient criteria for the existence of at least one periodic solution of the neural network systems. These results shown that there are still one or more periodic solutions for the neural networks with discontinuous activations under the impulsive effects. Moreover, sufficient criteria are given to the exponential periodic synchronization under the switching state-feedback control strategy with or without delay. Finally, two numerical simulation examples are presented to verify the correctness and validity of our main conclusions.

Event-Triggered Switching-Type Fault Detection and Isolation for Fuzzy Control Systems Under DoS Attacks

This article investigates the memory adaptive event-triggered fault detection and isolation (FDI) problem for nonlinear networked control systems under periodic denial-of-service (DoS) attacks, where the nonlinear systems are described by Takagi–Sugeno (T–S) fuzzy models with unknown membership functions. First, a novel event-triggered mechanism is proposed to save communication resources. The triggering threshold is adaptively adjusted by multiple previous sampled data, not only depending on the latest triggering data. Second, taking DoS attacks, and event-triggered mechanism into consideration, a switching state-feedback controller is established, and the exponential stability is derived. Meanwhile, the controller, and the event-triggered mechanism are simultaneously developed based on a piecewise Lyapunov function. Then, a set of switching T–S fuzzy observers are constructed to realize FDI under DoS attacks. Besides, a switching variable method is introduced to address the asynchronous premise variables problem caused by the event-triggered mechanism. Finally, simulation cases are given to demonstrate the validity, and merit of the proposed FDI scheme.

Robust state feedback for uncertain 2-D discrete switched systems in the Roesser model

The design of robust controllers is considered here for a class of two-dimensional (2-D) discrete switched systems described by the Roesser model with polytopic uncertainties. Attention focuses on the design of a switched state feedback controller, which guarantees the robust asymptotic stability and a prescribed performance for the closed-loop system. By using multiple parameter-dependent Lyapunov functionals, and introducing some switched free-weighting matrices, a new sufficient condition for the robust performance analysis of uncertain 2-D discrete switched systems is developed. Furthermore, the design of switched state feedback controller is proposed in terms of linear matrix inequalities (LMIs). Illustrative examples are given to illustrate the effectiveness of the developed theoretical results.

Event-triggered synchronization in fixed time for semi-Markov switching dynamical complex networks with multiple weights and discontinuous nonlinearity

This paper is concerned with on the event-triggered synchronization in fixed time for semi-Markov switching dynamical complex networks with multiple weights and discontinuous nonlinearity. Firstly, the principle of the global convergence in fixed time with respect to nonlinear systems with semi-Markov switching is developed. Secondly, in order to realize the global stochastic synchronization goal in fixed time, a novel hybrid controller, which is composed of the event-triggered controller and the switching state-feedback controller, is designed. Under Filippov differential inclusion framework, by applying Lyapunov functional method and inequality analysis technique, the global stochastic synchronization conditions in fixed time are achieved in the form of linear matrix inequalities (LMIs). In addition, the upper bound of the stochastic settling time, which is adjusted in advance by choosing the controller parameters, is estimated accurately. Finally, the correctness of the theoretical results and the feasibility of the designed controller are verified by an example.

Graph-Theoretic Approach to Finite-Time Synchronization for Fuzzy Cohen–Grossberg Neural Networks with Mixed Delays and Discontinuous Activations

This paper investigates finite-time synchronization for fuzzy Cohen–Grossberg neural networks (FCGNNs) with mixed delays and discontinuous activations via state-feedback control. The features of FCGNNs, discrete time delays, distributed delays and discontinuous activations are taken into account which makes our networks more general and practical in comparison with the most existing Cohen–Grossberg neural networks. Two switching state-feedback controllers designed for the implement of finite-time synchronization can be used to effectively overcome the limitations of the traditional continuous linear feedback controllers. Different from previous work, graph theory and Lyapunov method are used to study finite-time synchronization of FCGNNs for the first time in this paper, then some sufficient criteria are obtained to guarantee the finite-time synchronization of FCGNNs. In particular, it is worth noting that the settling time for finite-time synchronization is closely related to the topological structure of FCNNs. Finally, two numerical examples are given to verify the feasibility and effectiveness of the theoretical results.

Incremental passivity and stabilization for switched nonlinear systems

This paper studies the problems of incremental passivity, incremental passification and incremental stabilization for a switched nonlinear system. First, an incremental passivity concept for switched nonlinear systems is proposed. Each subsystem is only required to be incrementally passive, when it is active. The energy change of each inactive subsystem is charaterized. Then, a sufficient condition for such a system to be incrementally passive is given. Second, a state-dependent switching law and state feedback controllers are designed to render a system with relative degree one incrementally passive. Third, we show that an incrementally passive switched nonlinear system can be incrementally stabilized under some constraints on the energy change of inactive subsystems. In particular, a recursive feedback incremental passification design technique is adopted to achieve the incremental stability for a switched nonlinear system with any same relative degree by designing a set of feedback controllers and a state-dependent switching law, constructively. Finally, two examples are provided to verify the effectiveness of the proposed theory.

Event-triggered stochastic synchronization in finite time for delayed semi-Markovian jump neural networks with discontinuous activations

In this paper, the global stochastic synchronization in finite time is discussed for discontinuous semi-Markovian switching neural networks with mixed time-varying delays under stochastic disturbance based on event-triggered non-fragile control scheme. By applying the novel hybrid controller, which is composed of the event-triggered controller, the non-fragile controller and the switching state-feedback controller, the global stochastic synchronization goals in finite time are achieved. Under Filippov differential inclusion framework, based on non-smooth analysis theory, general free-weighting matrix method, Lyapunov–Krasovskii functional approach and inequality analysis technique, the global stochastic synchronization conditions in finite time are addressed in terms of linear matrix inequalities. Moreover, the expressions about the upper bound of stochastic settling time are explicitly developed. Finally, two numerical examples are provided to illustrate the feasibility of the proposed control scheme and the validity of theoretical results.

Finite-time stabilization and [formula omitted] control for a class of switched nonlinear port-controlled Hamiltonian systems subject to actuator saturation

This paper addresses the problems of finite-time stabilization and H∞ control for a class of switched port-controlled Hamiltonian (SPCH) systems with actuator saturation (AS). By the energy-based multiple Lyapunov functions (MLFs) method and the mode-dependent average dwell time (MDADT) technique, finite-time stability criterion for unforced SPCH systems with all modes finite-time stable is derived. Further, state feedback strategies and truncation inequality technique are employed to achieve finite-time stabilization of SPCH systems with AS, where each unforced subsystem may be finite-time unstable. Besides, a switching state feedback controller is developed to attenuate the external disturbances for SPCH systems with AS and external disturbances, and new criterion is presented to solve the finite-time H∞ control problem for the augmented system. Finally, numerical examples are provided to show the effectiveness of the proposed methods.

Stabilisation and ℋ∞ control for switched port-controlled Hamiltonian systems with unstable modes and actuator saturation

ABSTRACTIn this paper, the problems of stabilisation and control are addressed for switched port-controlled Hamiltonian (SPCH) systems with unstable modes and actuator saturation (AS) via energy-based multiple Lyapunov functions methods. Firstly, by a switching state feedback controller with truncation-inequality techniques, the considered system is transformed into an unforced SPCH system with asymptotically stable, stable and unstable modes. Then, by developing an alternative switching law with slow/fast mode-dependent average dwell time (MDADT) switching scheme, new sufficient conditions are obtained for stabilisation of the SPCH system. Secondly, by designing a new switching feedback controller, revealing the characteristics of alternative switching signals and defining an indicative function, a new criterion for control of the SPCH systems with unstable modes and AS is achieved via the slow/fast MDADT switching scheme. Moreover, based on the obtained results and the indicative function, control conditions for the corresponding SPCH system are also derived under a slow MDADT switching scheme and a traditional average dwell time scheme, respectively. Finally, some numerical examples are given to verify the effectiveness of the proposed methods.

Periodicity and stabilization control of the delayed Filippov system with perturbation

By employing Leray-Schauder alternative theorem of set-valued maps and non-Lyapunov method (non-smooth analysis, inequality analysis, matrix theory), this paper investigates the problems of periodicity and stabilization for time-delayed Filippov system with perturbation. Several criteria are obtained to ensure the existence of periodic solution of time-delayed Filippov system by using differential inclusion. By designing appropriate switching state-feedback controller, the asymptotic stabilization and exponential stabilization control of Filippov system are realized. Applying these criteria and control design method to a class of time-delayed neural networks with perturbation and discontinuous activation functions under a periodic environment. The developed theorems improve the existing results and their effectiveness are demonstrated by numerical example.

Composite control for switched impulsive time-delay systems subject to actuator saturation and multiple disturbances

This paper focuses on the composite control problem for a class of uncertain switched impulsive systems with time-varying time delay, actuator saturation and multiple disturbances which are matched and mismatched with continuous control inputs. The system under consideration involves parameter uncertainties and nonlinear uncertainties, and the actuators of both continuous control inputs and impulsive control inputs are considered to be limited by saturation. Actuator saturation brings great difficulties and challenges to implement composite control based on disturbance compensation, especially when the system is with matched disturbances. A novel switching composite controller and a switching state feedback controller are constructed respectively such that the performance requirement of anti-disturbance control for the system is achieved, the former of which can realize rejection of the matched disturbances simultaneously. Based on the treatment of the saturation as polytopic differential inclusion, the design conditions of the controllers are developed to guarantee the locally robustly asymptotic stability and robust H∞ disturbance attenuation of the closed-loop system with an estimation of the domain of attraction. Finally, a simulation example is performed to validate the feasibility of our results.

Stochastic [formula omitted] finite-time control of networked cascade control systems under limited channels, network delays and packet dropouts

Communication channel in the control loop brings new challenging topics that cause the controller design for the system very complicated. Data packet dropout, delay and limited channel are the main inevitable problems that can significantly degrade the system performance. Besides, stability analysis of such systems over infinite time interval using the Lyapunov stability concept imposes significant restrictions in practice due to control input saturation. The purpose of this paper is to introduce a control algorithm for stabilizing the discrete-time networked cascade control systems to suppress the detrimental effects of limited channel, delay and data packet dropout by means of finite-time H∞ control. Non-uniformly distributed nature of the delay together with packet dropout are modeled as a Bernoulli distributed white sequence. Finite-time boundedness and stochasticH∞finite-time stability are demonstrated by designing a switching state-feedback controller. Simulations are given to show the proposed controller under the network imperfections.