Non-fragile State Feedback Controller Research Articles

Non-fragile projective synchronization of delayed discrete-time neural networks via generalized weighted summation inequality

This paper explores the problem of exponential projective synchronization (EPS) for delayed discrete-time uncertain neural networks (NNs) subject to non-fragile state feedback control. To attain less conservative results, some generalized weighted summation inequalities are proposed, which encompass Jensen-based summation inequality (JBSI) as its special case. By constructing suitable Lyapunov-Krasovskii functional (LKF), sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to ensure the EPS via newly introduced weighted summation inequalities. Finally, numerical examples are provided, supported by simulation results through MATLAB software that ensures the efficiency of the desired theoretical outcomes and the comparative study in terms of maximum allowable upper bound (MAUB) evaluates the effectiveness of the established results by enhancing the feasible region.

Exponential stability for switched semi‐Markov jump systems with mode‐dependent average dwell time and generally uncertain transition rates

AbstractThis paper investigates the exponential stability in mean square sense for a class of stochastic switched semi‐Markov jump systems (ssSMJS). In this model, a hierarchical control switched regulation is designed, considering the external stochastic disturbances and generally uncertain transition rates (TRs) of the entire system and making the system more general and practical. By using appropriate Lyapunov–Krasovskii functional, linear matrix inequality, Jensen inequality, and mode‐dependent average dwell time (MDADT), sufficient conditions on the exponential stability in mean square sense for ssSMJS are derived. Furthermore, a nonfragile state feedback controller is designed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed criterion.

Passive and H ∞ control based on non-fragile observer for a class of uncertain nonlinear systems with input time-delay

In this paper, passive control and H ∞ state feedback based on non-fragile observer are presented for a class of uncertain, nonlinear and input time-delay systems. Firstly, taking uncertainties, nonlinearities and input time-delay into account, non-fragile observer and controller are designed and the perturbations of controller gain and observer gain are processed. Secondly, for the dynamic disturbances, an appropriate non-fragile state feedback controller based on the observation is selected to prove that the states of closed-loop system can be passive and stabilized with H ∞ performance for continuous time system. Moreover, the problems such as time-delay are handled in virtue of Lyapunov method and linear matrix inequalities (LMIs). Finally, the simulation results demonstrate the validity of the proposed control design method.

Further improvement of finite-time boundedness based nonfragile state feedback control for generalized neural networks with mixed interval time-varying delays via a new integral inequality

This article investigates new delay-dependent finite-time boundedness for generalized neural networks (GNNs) with mixed-interval time-varying delays based on nonfragile feedback control to achieve the improved stability criterion. We also propose a new integral inequality with an exponential function to estimate the derivative of the Lyapunov–Krasovskii functional (LKF). Furthermore, the well-known Wirtinger’s inequality is a particular case of the new integral inequality. Using a toolbox optimization in MATLAB, we derive and solve new delay-dependent conditions in terms of linear matrix inequalities (LMIs). Additionally, we give three numerical examples to show the advantages of our obtained methods. The examples can apply the continuous time-varying delays that do not need to be differentiable. One of them presents the benchmark problem’s real-world application, which is a four-tank system.

Non-fragile guaranteed cost control of nonlinear switched systems with actuator saturation

This paper considers a non-fragile guaranteed cost control problem for a class of nonlinear switched systems with actuator saturation. For nonlinear switched systems, we derive some sufficient conditions to satisfy simultaneously the stabilization and the performance index of guaranteed cost control. To ensure the asymptotic stability of the nonlinear switched systems and minimize the upper bound of cost function, a switching law and non-fragile state feedback controllers are designed using the multiple Lyapunov functions method. On this basis, an optimization problem is solved by adopting linear matrix inequality (LMI) constraints, and the minimum upper bound of cost function is determined. At the end of the paper, a numerical example is given to prove the effectiveness of the proposed method.

Nonfragile robust exponential stabilization of nonlinear uncertain switched systems with actuator saturation

AbstractFor nonlinear uncertain switched systems, the problem of how to overcome the controller vulnerability is studied when the actuator saturation is considered. The sufficient condition for guaranteeing nonfragile robust exponential stabilization of the system is derived by using the method of minimum dwell time. Then, a switching law and the nonfragile state feedback controllers are designed such that the closed‐loop system can be robustly exponentially stabilized at the origin. Next, when some scalar parameters of the closed‐loop system are given, the design issue of the nonfragile state feedback controllers, which aim at enlarging the estimation of domain of attraction for closed‐loop system, is transformed into a convex optimization issue with linear matrix inequalities (LMI) constraints. Finally, an example is given to verify the effectiveness of the proposed method.

Formal synthesis of non-fragile state-feedback digital controllers considering performance requirements for step response

This work describes an approach for synthesizing state-feedback controllers for discrete-time systems, taking into account performance aspects. The proposed methodology is based on counterexample-guided inductive synthesis (CEGIS), producing safe controllers based on step response performance requirements, such as settling time and maximum-overshoot. Controller candidates are generated through constrained optimization based on genetic algorithms. Each iteration that does not satisfy the initial system requirements is learned as a failed result and then used in another attempt. During the verification phase, it is considered the controller fragility to ensure deployable implementations. Such an approach assists the discrete-time control system design since weaknesses occur during implementation on digital platforms, where systems that meet design requirements are employed. The proposed method is implemented in DSVerifier, a tool that uses bounded (and unbounded) model checking based on satisfiability modulo theories. Experimental results showed that our approach is practical and sound regarding the synthesis of discrete state-feedback control systems that present performance requirements. It considers finite word-length effects, unlike other methods that routinely ignore them.

Non-fragile extended dissipative synchronization control of delayed uncertain discrete-time neural networks

This article is concerned with the problem of robust extended dissipative synchronization for a class of delayed discrete-time neural networks through non-fragile state-feedback control. For this notion, we propose a new summation inequality based on extended reciprocally convex matrix inequality to linearize the quadratic summable terms induced through the finite-difference of the constructed Lyapunov–Krasovskii functional. By utilizing this derived inequality, the sufficient condition ensures the less conservative robust extended dissipativity performance is obtained in terms of linear matrix inequalities subject to both additive and multiplicative norm-bounded uncertainty. Finally, numerical examples are performed to acknowledge the significance and efficiency of the proposed theoretical results.

Finite-time mixed [formula omitted] and passivity analysis for Takagi–Sugeno fuzzy system with time-varying delays and actuator faults

This paper comes up with an novel augmented Lyapunov–Krasovskii functional (LKF) approach to process finite-time passivity-based H∞ non-fragile state feedback control issue of Takagi–Sugeno fuzzy system (TSFS) via taking the effects of both time-varying delays and actuator faults. Designing a non-fragile controller to guarantee that TSFS is finite-time bounded (FTB) and meet finite-time mixed H∞ and passive performance is the focus of this paper. On the basis of the new augmented LKF and improved boundary techniques, sufficient delay-dependent conditions are inferred to acquire the desired results of the TSFS. Furthermore, the derived finite-time stability conditions are derived in terms of linear matrix inequalities (LMIs) and the controller gain matrices are confirmed through solving LMIs. Subsequently, three examples are addressed to certify the applicability and advantage of the put forward methodology.

Non-fragile stabilisation of nonlinear switched systems with actuator saturation

For nonlinear continuous-time switched systems, the problem of how to overcome the controller vulnerability is studied when the saturating actuator is considered. The sufficient condition of non-fragile stabilisation of the system is derived by using the method of multiple Lyapunov functions. Then, a switching law and the non-fragile state feedback controllers are designed such that the closed-loop system can be asymptotically stabilised at the origin. Finally, when some scalar parameters of the closed-loop system are given, the design issue of the non-fragile state feedback controllers and the switching law, which aim at enlarging the estimation of domain of attraction for closed-loop system, is transformed into a convex optimisation issue with linear matrix inequalities (LMI) constraints, and a numerical example is given to verify the effectiveness of the proposed method.

Non‐fragile H∞ control for LPV‐based CACC systems subject to denial‐of‐service attacks

This paper is concerned with a non-fragile H ∞ state feedback control issue for linear parameter-varying collaborative adaptive cruise control systems subject to denial-of-service attacks. The dynamics of the collaborative adaptive cruise control system is described by a linear model where the deviation of the position and the velocity are selected as the state variables. The attack model is utilized, thereby better reflecting the randomly occurring phenomenon of the denial-of-service attacks based on a sequence of binary random variables. The main objective of this note is to develop a non-fragile state feedback control scheme such that, for denial-of-service attacks and possible parameter variations in controller gains, the exponential mean-square stability and the predefined performance index for the system states are guaranteed simultaneously. By using the matrix analysis techniques and Lyapunov stability theory, sufficient conditions for the desired controller are established and solved based on the solutions to the linear matrix inequality conditions. Finally, a three-car model is provided to check the feasibility of the designed control scheme.

Robust non-fragile memory feedback control for multi-weighted complex dynamical networks with randomly occurring gain fluctuations

This paper deals with the robust observer-based synchronisation problem for a class of complex dynamic networks subject to multi-weights, time-varying coupling delay and external disturbance. Specifically, the gain fluctuation appears in the proposed controller and is represented in terms of a random variable obeying the Bernoulli distribution. The main objective of this paper is to design a non-fragile memory state feedback controller such that the resulting error system is stochastically synchronised under a prescribed performance level . First, a Luenberger-type state observer is constructed to estimate the state variables of the addressed system. Second, by constructing an appropriate Lyapunov–Krasovskii functional and using Wirtinger-based integral inequality techniques, the required set of sufficient conditions for the synchronisation of the proposed system is established in the form of linear matrix inequalities. In the end, two numerical examples are provided to demonstrate the validity and feasibility of the developed theoretical results.

Non‐fragile control for a class of fractional‐order uncertain linear systems with time‐delay

This study addresses the non-fragile controller design of a class of fractional-order (FO) linear delayed systems assumed to have structured uncertainties in both the plant and the controller. By using the linear matrix inequality method, singular value decomposition and FO Razumikhin theorem, the delay-dependent and order-dependent robust non-fragile state feedback controller and non-fragile observer-based robust state feedback controller are synthesised, respectively, based on whether the states are available or not. Three examples are presented to verify the effectiveness of the proposed schemes.

Non-fragile memory feedback control for uncertain time-varying delay switched fuzzy systems with unknown nonlinear disturbance

Currently, the feedback control rate of most nonlinear systems is realised by the memoryless state feedback controller which cannot affect the impact of time delay on the systems, and the general processing method of the Lyapunov–Krasovskii functional for the time-varying delay switched fuzzy systems (SFS) is more conservative. Therefore, this paper addresses the problem of non-fragile robust and memory state feedback control for switched fuzzy systems with unknown nonlinear disturbance. Non-fragile memory state feedback robust controller which has two controller gains different from each other, and switching law are designed to keep the proposed systems asymptotically stable for all admissible parameter uncertainties. Delay-dependent less conservative sufficient conditions are obtained through using the Lyapunov–Krasovskii functional method and free-weighting matrices depending on Leibniz–Newton, guaranteeing that the SFS can be asymptotically stable. A numerical example is given to illustrate the proposed controller performs better than the classic memoryless state feedback controller.

Design of Non-fragile Controller for Singular Fractional Order Takagi–Sugeno Fuzzy Systems

This paper investigates the stabilization problem of a class of singular fractional order fuzzy systems with order $$0<\alpha <1$$ . Firstly, by the method of full rank decomposition of matrix, equality constraint of admissibility criterion in most existing literature is eliminated. Next, we present a stabilization criterion for singular fractional order Takagi–Sugeno (T–S) fuzzy systems by designing non-fragile state feedback controllers. Then, applying an equivalent form of original system in admissibility, the non-fragile output feedback controllers are designed to guarantee the closed-loop systems stable. And for fractional order $$1<\alpha <2$$ case, using similar designing approaches, strict linear matrix inequality (LMI) stabilization criteria based on non-fragile state and output feedback controller are obtained. Finally, two numerical simulation examples are given to illustrate the effectiveness of the proposed method.

Non-fragile extended dissipative control for event-triggered networked stochastic systems

ABSTRACTThis paper investigates the problem of extended dissipative analysis based non-fragile controller for networked stochastic system under an event-triggered sampling scheme. First, we introduce an event-triggered scheme and the proposed system is modelled as a stochastic time-delay system. By multi-delay partitioning method, some delay-dependent criteria in terms of linear matrix inequality are proposed to ensure the mean-square stable with extended dissipative performance, where using the notion of the extended dissipative, we can solve (Q, S, R)-dissipativity, , passivity and performance in a unified framework by regulating some weight matrices. In addition, two non-fragile state feedback controllers are designed to ensure that the closed-loop system satisfies the extended dissipative performance. Finally, some simulation examples are given to substantiate the validity of the addressed method.

Improved Non-Fragile State Feedback Control for Stochastic Jump Systems With Uncertain Parameters and Mode-Dependent Time-Varying Delays

This paper reports the investigation on non-fragile state feedback control for stochastic Markovian jump systems with uncertain parameters and mode-dependent time-varying delays. The resulted closed-loop system is stochastic stabilization by virtue of an improved L-K functional. By free-weight-matrix technique, the non-fragile state feedback controller is designed and novel conditions for robust stochastic stabilization are acquired in the form of linear matrix inequalities. Two examples including a take-off and landing guidance system are employed to show the effectiveness and validity of the proposed approach.

Multiobjective nonfragile fuzzy control for nonlinear stochastic financial systems with mixed time delays

In this study, a multiobjective nonfragile control is proposed for a class of stochastic Takagi and Sugeno (T–S) fuzzy systems with mixed time delays to guarantee the optimal H2 and H∞ performance simultaneously. Firstly, based on the T–S fuzzy model, two form of nonfragile state feedback controllers are designed to stabilize the T–S fuzzy system, that is to say, nonfragile state feedback controllers minimize the H2 and H∞ performance simultaneously. Then, by applying T–S fuzzy approach, the multiobjective H2/H∞ nonfragile fuzzy control problem is transformed into linear matrix inequality (LMI)-constrained multiobjective problem (MOP). In addition, we efficiently solve Pareto optimal solutions for the MOP by employing LMI-based multiobjective evolution algorithm (MOEA). Finally, the validity of this approach is illustrated by a realistic design example.

Non-fragile passive control for Markovian jump systems with time-varying delays

This paper studies the problem of non-fragile passivity-based control for Markovian jump systems with time-varying delays. Based on a delay partitioning method, a modified Lyapunov–Krasovskii functional is constructed to derive sufficient conditions guaranteeing stochastic passivity of the considered systems. Moreover, a non-fragile state feedback controller is designed such that the closed-loop system is robustly stochastically passive. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.

Non-fragile saturation control of nonlinear positive Markov jump systems with time-varying delays

This paper investigates non-fragile saturation control of nonlinear positive Markov jump systems, which contain sector nonlinear functions and time-varying delays. The saturation controller to be designed is supposed to have either multiplicative or additive gain uncertainty. First, a sufficient condition for the positivity of an auxiliary nonlinear system with sector restriction is established. By employing a nonlinear co-positive-type Lyapunov functional, a non-fragile control of the considered systems with multiplicative and additive perturbations is proposed in terms of linear programming, respectively. A set of non-fragile state feedback controllers associated with auxiliary feedback gains is designed using a matrix decomposition technique. Based on the designed controllers, the corresponding closed-loop systems are positive and stable with an $$L_{1}$$ -gain performance and the system states converge to a cone set. Furthermore, an optimization method is developed to estimate the maximum invariant set. Compared with existing results, the proposed technique is not only less conservative but also reliable in practice. Finally, two simulation examples are provided to show the effectiveness of the obtained results.