Nonfragile fuzzy dynamic output feedback control for nonlinear systems with multiplicative gain uncertainty

This paper investigates the problem of event-triggered dynamic output feedback control for networked Takagi-Sugeno (T-S) fuzzy systems with asynchronous premise variables. Our attention is focused on the design of an event-triggered fuzzy dynamic output feedback controller that guarantees that the closed-loop system is asymptotically stable. First, with consideration of the limited bandwidth and restricted network resource, an event-triggered communication scheme is proposed to save the limited network resource. Second, different from the existing results in the literature, a fuzzy dynamic output feedback controller with asynchronous premise variables is constructed such that the premise membership functions are not necessarily the same as the networked T-S fuzzy systems. Then, by using the Wirtinger inequality and some slack matrices, a less conservative stability and stabilization conditions for the existence of fuzzy dynamic output feedback controller are derived in the form of linear matrix inequalities, which can be solved by the standard MATLAB toolbox. Finally, an example is given to demonstrate the effectiveness of the designed event-triggered fuzzy dynamic output feedback controller.

This paper concerns the problem of dynamic output-feedback control for a class of nonlinear systems with nonuniform uncertain sampling via Takagi-Sugeno (T-S) fuzzy control approach. The sampling is not required to be periodic, and the state variables are not required to be measurable. A new type fuzzy dynamic output-feedback sampled-data controller is constructed, and a novel time-dependent Lyapunov-Krasovskii functional is chosen for fuzzy systems under variable sampling. By using Lyapunov stability theory, a sufficient condition for very-strict passive analysis of fuzzy systems with nonuniform uncertain sampling is derived. Based on this condition, a novel fuzzy dynamic output-feedback controller is designed such that the closed-loop system is very-strictly passive. The existence condition of the controller can be solved by convex optimization approach. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

By utilising Takagi–Sugeno (T–S) fuzzy set approach, this paper addresses the robust H∞ dynamic output feedback control for the non-linear longitudinal model of flexible air-breathing hypersonic vehicles (FAHVs). The flight control of FAHVs is highly challenging due to the unique dynamic characteristics, and the intricate couplings between the engine and fight dynamics and external disturbance. Because of the dynamics’ enormous complexity, currently, only the longitudinal dynamics models of FAHVs have been used for controller design. In this work, T–S fuzzy modelling technique is utilised to approach the non-linear dynamics of FAHVs, then a fuzzy model is developed for the output tracking problem of FAHVs. The fuzzy model contains parameter uncertainties and disturbance, which can approach the non-linear dynamics of FAHVs more exactly. The flexible models of FAHVs are difficult to measure because of the complex dynamics and the strong couplings, thus a full-order dynamic output feedback controller is designed for the fuzzy model. A robust H∞ controller is designed for the obtained closed-loop system. By utilising the Lyapunov functional approach, sufficient solvability conditions for such controllers are established in terms of linear matrix inequalities. Finally, the effectiveness of the proposed T–S fuzzy dynamic output feedback control method is demonstrated by numerical simulations.

Stability analysis and dynamic output feedback controller design of T–S fuzzy systems with time-varying delays and external disturbances

New results on dynamic output state feedback stabilization of some class of time-varying nonlinear Caputo derivative systems

This paper addressed the fuzzy dynamic output feedback control problem for a class of nonlinear discrete-time Takagi–Sugeno (T-S) fuzzy systems with multiple time-varying delays and unmatched disturbances. Based on the control input matrix and output matrix, the T-S fuzzy model is employed to approximate the nonlinear discrete-time system. Based on the stochastic system theory and the Bernoulli distribution, the fuzzy dynamic output feedback controller is constructed for the nonlinear discrete-time T-S fuzzy system with multiple time-varying delay and unmatched disturbance. The $H_{\infty } $ performance analysis is presented, and the cone complementarity linearization algorithm is employed for the stability analysis to deal with the non-convex problem caused by the basis-dependent linear matrix inequalities conditions. Compared with the previous works, the developed controller in this paper is smooth and only uses the system output. The control design conditions are relaxed because of the developed cone complementarity linearization algorithm. The results are further extended to the chemical process case and the mobile robot case. Finally, two simulation examples are performed to show the effectiveness of the proposed methods.

This paper investigates the problem of passive dynamic output feedback control for fuzzy discrete nonlinear systems with quantization and actuator failures, where the measurement output of the system is quantized by a logarithmic quantizer before being transferred to the fuzzy controller. By employing the fuzzy-basis-dependent Lyapunov function, sufficient condition is established to guarantee the closed-loop system to be mean-square stable and the prescribed passive performance. Based on the sufficient condition, the fuzzy dynamic output feedback controller is proposed for maintaining acceptable performance levels in the case of actuator failures and quantization effects. Finally, a numerical example is given to show the usefulness of the proposed method.

Robust H∞ dynamic output feedback control for interval type-2 T-S fuzzy multiple time-varying delays systems with external disturbance

This paper addresses the problem of robust fuzzy dynamic output feedback control of a nonlinear discrete time system described by a Takagi -Sugeno fuzzy model. It is assumed that the system is subjected to actuator fault. First, the closed-loop faulty dynamic model of the system and the fuzzy dynamic output feedback controller are introduced. Then, the stability conditions are established via Lyapunov theory, which are formulated in terms of linear matrix inequalities to solve the problem. Finally, a numerical example is presented to illustrate the effectiveness of the proposed controllers.

This note addresses the problem of the assignability of the eigenvalues of the matrix <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A + BPC</tex> by choice of the matrix <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</tex> . This mathematical problem corresponds to pole assignment in the direct output feedback control problem, and by proper changes of variables it also represents the pole assignment problem with dynamic feedback controllers. The key to our solution is the introduction of the new concept of local complete assignability which in loose terms is the arbitrary perturbability, of the eigenvalues of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A + BPC</tex> by perturbations of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</tex> . If n <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> is the order of the system, we show that if <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A + BP_{0}C</tex> has distinct eigenvalues, a necessary and sufficient condition for local complete assignability at P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> is that the matrices <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C[A + BP_{0}C]^{i-1}B</tex> be linearly independent, for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1 \leq i \leq n_{x}</tex> . In special cases, this condition reduces to known criteria for controllability and observability. Although these latter properties are necessary conditions for assignability, we also address the question of the assignability of uncontrollable or unobservable systems both by direct output feedback and dynamic compensation. The main result of this note yields an algorithm that assigns the closed-loop poles to arbitrarily chosen values in the direct and in the dynamic output feedback control problems.

The H-infinity stability analysis and delay-dependent Takagi–Sugeno (T–S) fuzzy dynamic output feedback control are proposed for the T–S fuzzy discrete networked control systems with time-varying communication delay and multipath packet dropouts. T–S fuzzy model is employed to approximate the discrete networked control system with time-varying state delay and external disturbance. Stochastic system theory and Bernoulli probability distribution are employed to describe the time-varying communication delay and multipath packet dropouts. Delay-dependent T–S fuzzy dynamic output feedback controller is designed. The delay-dependent T–S fuzzy dynamic output feedback controller is employed to relax the design conditions and enhance the design flexibility. The delay-dependent Lyapunov–Krasovskii functional, stochastic system theory and Bernoulli probability distribution are introduced to guarantee the stochastic mean-square stability and prescribed H-infinity performance. Some slack matrices are introduced to reduce the computation complexity. Finally, simulation examples are presented to show the effectiveness and advantages of the proposed methods.

This study focuses on the problem of adaptive fuzzy dynamic surface output feedback control for a class of uncertain nonlinear systems subjected to unknown input hysteresis. A Prandtl–Ishlinskii (PI) model is applied to the uncertain nonlinear system for describing the unknown input hysteresis, making the controller design feasible. In addition, a nonlinear extended state observer (NESO) is designed for simultaneously estimating the unmeasurable states and generalized disturbances, including the nonlinear hysteresis term of the PI model and external disturbances. In addition, a novel nonlinear function is designed to replace the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$fal(\cdot)$</tex-math></inline-formula> function of the general NESO to address a modification that increases the convergence speed. Considering the incorporation of the improved nonlinear extended state observer (INESO), an adaptive output feedback control scheme is proposed based on fuzzy logic system and dynamic surface techniques. A command filter is employed to avoid the “explosion of complexity” problem inherent in the backstepping technique, while compensating the filtering error caused by adopting the filter. The Lyapunov approach is used to demonstrate the stability of the entire closed-loop system. Experiments regarding a piezoelectric micro–positioning stage are conducted, the results of which illustrate that the proposed adaptive fuzzy output feedback control method can guarantee a satisfactory tracking performance.

In this paper, H ∞ dynamic output feedback control for discrete-time nonlinear stochastic T-S fuzzy model with state-dependent noise is attacked. We consider the fuzzy T-S models has has stochastic uncertainties, i.e., state-dependent noise, in the system matrix, input matrix, and output matrix. First, when the premise variables in the fuzzy plant model are available, an H ∞ fuzzy dynamic output feedback controller, which uses the same premise variables as the T-S fuzzy model, is proposed for regulation of the controlled system to meet the H ∞ control performance specification. Next, when the premise variables for building the fuzzy plant model are not available, a fuzzy H, observer-based state feedback controller, in which the premise variables are the estimated version of the premise variables in the T-S fuzzy model, is proposed. For the two cases, we conduct sufficient conditions described by linear matrix inequalities (LMI) to ensure stability of the closed-loop system. Performance of the proposed fuzzy controller is verified by simulation study.

This paper considers dynamic feedback stabilization for abstract second‐order systems, where the dynamic feedback controller is designed as another abstract second order infinite/finite‐dimensional system. This makes the closed‐loop system PDE‐PDE or PDE‐ODE coupled. The stability of the closed‐loop system is found to have three different cases. We first consider the dynamic feedback control in a general Hilbert space which is usually different from the control space. It is shown that the stability of the closed‐loop systems under the dynamic and static feedbacks are usually not equivalent. However, if the dynamic control law is a copy of the original system, we deduce, under some conditions, that the coupled system is exponentially stable if and only if the static feedback closed‐loop system is exponentially stable. When the dynamic feedback is designed in the control space, the closed‐loop system is asymptotically stable if and only if static feedback closed‐loop system is asymptotically stable.

This paper is concerned with the event-triggered dynamic output feedback control for linear time invariant (LTI) systems subject to actuator saturation. Firstly, a novel event-triggered scheme and dynamic output feedback controller are presented. Under the proposed framework: (a) the samplings of the sensor are designed as specific time-varying signals utilizing exponentially decaying function; (b) the dynamic feedback controller is equipped with an anti-windup compensator; (c) a lower bound of the inter-event interval is derived to exclude the Zeno behavior. Secondly, by constructing Lyapunov function and generally sector condition, some sufficient stability criteria are derived via linear matrix inequalities. Thirdly, depend on the stability criteria and MATLAB LMI toolbox, the parameters of event-triggered scheme and the controller are calculated. Finally, the effectiveness of the proposed method is illustrated by a numerical example.