Delay-dependent Stability Conditions Research Articles

Switched sampled-data-based membership function-dependent [formula omitted] control for PMSG-based WTS with actuator failures

This paper deals with the problem of sampled-data-based H∞ control design for nonlinear permanent magnet synchronous generator (PMSG)-based wind turbine system (WTS) subject to actuator failures. First, the Takagi-Sugeno (T-S) fuzzy system is employed to handle the nonlinearities of presented model. Next, by employing a Bernoulli stochastic variable, the general scenario of switched coupling memory sampled-data control (CMSDC) is designed which contains the sampled-data control (SDC) and memory SDC scheme as special cases. By combining the membership function-dependent (MFD) asymmetric looped-type Lyapunov-Krasovskii functional (LKF) and employing the available information of membership functions in H∞ performance, the delay-dependent stabilization conditions of considered PMSG-based WTS are derived through the switched CMSDC technique. Meanwhile, the disturbances of considered systems are attenuated by taking the advantage of the newly proposed MFD H∞ performance. Eventually, the simulation results are given to demonstrate the efficacy and applicability of the proposed CMSDC technique.

Improved results for T-S fuzzy systems with two additive time-varying delays via an extended binary quadratic function negative-determination lemma

This paper is concerned with the stability and stabilization problems for T-S fuzzy systems with two additive time-varying delays. Firstly, a novel Lyapounov-Krasovskii functional (LKF) is constructed by delay-product-type functional method together with the state vector augmentation. In order to handle time-delay square terms introduced into the derivative of LKF, an extended binary quadratic function negative-determination lemma is proposed. A less conservative delay-dependent stability condition is developed since not only some new bounding technologies are employed to deal with integral terms, but also the proposed lemma is employed to dispose nonlinear time-delay terms in derivative of constructed function. Then, the corresponding controller design method for closed-loop delayed fuzzy system is derived based on parallel distributed compensation scheme. Finally, four numerical examples are given to illustrate the superiority and effectiveness of the proposed criteria.

Flexible Quadrotor Unmanned Aerial Vehicles: Spatially Distributed Modeling and Delay-Resistant Control

This paper introduces an analytical framework for the derivation of distributed-parameter equations of motion of a flexible quadrotor. This approach helps obtain rigid and elastic equations of motion simultaneously, in a decoupled form, to facilitate the controller design. A delay-resistant low-frequency adaptive controller is employed, which prevents excessive oscillations due to flexible dynamics, compensates uncertainties, and addresses the inherent time delay. In addition to this, a delay-dependent stability condition for the overall system dynamics is obtained including the human operator with reaction time delay, the adaptive controller, and the flexible quadrotor dynamics with input delay. With comparative simulation studies, it is demonstrated that the flexible arm tip oscillations are significantly reduced when the low-frequency delay-resistant closed-loop reference model adaptive controller is used, compared to a closed-loop reference model adaptive controller and a conventional model reference adaptive controller.

Order-Dependent Sampling Control of Uncertain FO Linear System

This paper proposes a sampled-data control problem for the fractional-order system with parameter uncertainties. First, according to the input delay approach, the dynamics of the considered fractional-order system is modeled by a delay system. The main purpose of the problem addressed is to design a sampled-data controller, such that the closed-loop fractional-order system guarantees the asymptotic stability. Then, the Lyapunov-Krasovskii functional is constructed to derive the stable criterion. The new delay-dependent and order-dependent stability conditions are presented in the form of linear matrix inequalities. Eventually, a new sampled-data controller is designed to ensure the stability and stabilization of fractional-order system. Finally, a numerical example is given to illustrate the effectiveness and superiority of the derived criterion.

Observer-based fuzzy integral sliding mode control for bilateral teleoperation systems with time-varying delays

This paper aims to examine the stability and tracking performance of a bilateral teleoperation system. The Takagi–Sugeno fuzzy method is utilized, through which the nonlinear master–slave dynamics is converted as a fuzzy-based system. The state observers are designed for the linearized fuzzy teleoperation systems, and the corresponding estimation errors are formulated. Importantly, a novel observer-based fuzzy integral sliding mode control is developed by deliberately introducing the delay term into the sliding surfaces. As such, advanced delay-product type of Lyapunov–Krasovskii functionals are constructed for the augmented state vectors, in order to acquire the additional delay information. In addition, the Wirtinger-based integral inequality along with an extended reciprocally convex matrix inequality is applied to the Lyapunov derivatives to establish the delay-dependent stability conditions. Numerical results are provided to demonstrate efficacy of the developed control mechanism.

LMIs-based exponential stabilization for interval delay systems via congruence transformation: Application in chaotic Lorenz system

This paper investigates the stochastic Takagi-Sugeno (T-S) fuzzy uncertainty-dependent state feedback sampled-data control, asymptotical stability and exponential stability analysis for a class of stochastic T-S fuzzy system with measurable uncertainties, mixed interval time varying delays and Gaussian white noise. Firstly, the T-S fuzzy model and stochastic Bernoulli theory are employed to approximate the system plant. Secondly, the stochastic T-S fuzzy uncertainty-dependent state feedback sampled-data controller is designed via uncertainty-dependent parameters and the hold times series of sampled-data. Thirdly, the Bernoulli probability distribution is employed to describe the random occurrence characteristic of multipath packet dropouts. Three classes of delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) are derived for the closed-loop system. The multiple integral fuzzy-basis-dependent Lyapunov functional and augmented state variable are employed to derive the delay-dependent stability conditions, then the closed-loop system is asymptotically stable and exponentially stable. The congruence transformation method and prescribed H-infinity performance functional are employed to derive the less conservative delay-dependent stability conditions, and the prescribed H-infinity performance is guaranteed. The relaxation matrix and congruence transformation method are employed to design the linear transformation equalities and congruence transformation matrices, then the controller gain matrix is determined and computation complexity of solving LMIs is reduced. Finally, the proposed method is applied in the chaotic Lorenz system to show the effectiveness and advantage of proposed method.

Enhanced Exponential Stability Analysis for Switched Linear Time-Varying Delay Systems Under Admissible Edge-Dependent Average Dwell-Time Strategy

This article focuses on the exponential stability analysis for the switched linear systems with time-varying delay. By constructing a new augmented multiple Lyapunov–Krasovskii functional, containing time-varying delay information, coupling of current and delayed states, state integral, and state derivative terms the feasibility of the stability condition is considerably enhanced. Besides, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$</tex-math> </inline-formula> -order canonical Bessel–Legendre integral inequality and the convex function property are utilized to give more relaxed criteria. On the other hand, for the first time, more flexible switching is employed with an admissible edge-dependent average dwell-time strategy for the switched time-varying delay systems (STDSs). Novel improved delay-dependent stability conditions are expressed by two theorems in the form of linear matrix inequalities which can be used to guarantee the exponential stability of the STDSs in the different delay conditions. Finally, significant improvements over the state-of-the-art in terms of delay upper bound, exponential decay rate, and dwell time are presented by simulating two numerical examples and one practical example including streams water quality preserving.

Improved delay-dependent stability conditions for discrete-time neural networks with time-varying delays

Improved delay-dependent stability conditions for discrete-time neural networks with time-varying delays

Delay-dependent stability conditions for differential–difference equations with small commutators in a banach space

Let [Formula: see text] and [Formula: see text] be bounded operators in a Banach space. For the equation [Formula: see text] we derive sharp explicit delay-dependent exponential stability conditions via the commutator [Formula: see text]. The stability conditions in terms of the commutator enable us to construct a feedback with delay, which stabilizes a system. Gives us a possibility construct Stabilization of Systems with Retarded Feedback in a Banach Space. Our results are new even in the finite-dimensional case.

Performance and robustness trade-offs in PIR control of uncertain second-order systems with input disturbances

We investigate the robustness, disturbance attenuation and performance capabilities of a Proportional-Integral-Retarded (PIR) controller when controlling a class of uncertain second-order systems with input disturbances. The purpose of this paper is to provide insight into the trade-offs between these conflicting requirements. This is accomplished by introducing simple delay-dependent stability conditions, expressed in linear matrix inequality form, which are used to establish the trade-offs in PIR control. In light of the obtained stability conditions, we show that improving performance comes at the cost of reduced robustness and disturbance attenuation. To our knowledge, this problem has not been addressed before and these new results provide valuable insights and systematic guidelines for designing these controllers with trade-offs in mind, thereby completing our current understanding of the tuning mechanisms in PIR control. Inspired by the application field of fuel-cell systems, experiments are carried out on a proof-of-concept switching converter prototype to demonstrate the relevance of the obtained results.

Practical consensus for heterogeneous multi-agent systems with gain fluctuations via resilient sampled-data control

This study proposes a sampled-data-based practical consensus control method for heterogeneous multi-agent systems with gain fluctuations. First, the heterogeneous multi-agent system is formulated together with randomly occurring nonlinear dynamics. Second, unlike the existing studies, a more general retarded sampled-data control approach is designed, which involves the gain fluctuations along with the actual sampling pattern and constant time delay, to achieve the practical consensus of the considered system. By utilizing the aperiodic sampling information, and looped functional approach, a Wirtinger’s inequality-based discontinuous Lyapunov-Krasovskii functional is constructed to derive the delay-dependent stability condition of the closed-loop system in the form of linear matrix inequality. Finally, numerical simulation is presented to illustrate the derived theoretical results.

Delay-dependent and order-dependent asymptotic stability conditions for Riemann–Liouville fractional-order systems with time delays

Delay-dependent and order-dependent asymptotic stability conditions for Riemann–Liouville fractional-order systems with time delays

Stabilization of nonlinear fractional order faulty systems with time-varying delay

This paper focuses on the issue of stabilization of nonlinear fractional order time-delay systems in the presence of fault. A general class of nonlinear fractional order systems is considered in which fault causes variations in the system dynamic and actuators. Besides, time-varying delay is noticed in the system equations that is of high importance in control of real-life systems. In order to facilitate the problem of controller design for such systems, a precise method for modeling complex nonlinear systems, namely, Takagi–Sugeno fuzzy model, is adopted. Regarding a Caputo derivative–based Lyapunov–Krasovskii functional, new delay-dependent stabilization conditions are established in the form of linear matrix inequalities. Eventually, two examples including a truck–trailer and Lorenz system are simulated in order to evaluate the results of this research work.

Delay-Dependent Stability Condition in Finite Frequency Domain: Input-Output Approach

Over finite frequency ranges, this study analyzes delay-dependent stability criteria for time-varying delay systems. To develop new delay-dependent stability conditions in finite frequency domains for the continuous time-varying delay systems, we construct an input-output technique for delay-dependent systems utilizing the two-term transformation model paired with Scaled-Small Gain (SSG) approach. Sufficient conditions are obtained and described in terms of linear matrix inequalities (LMIs) constraints based on a novel delay-dependent finite frequency inequality. As an illustration, a numerical example has been supplied to test the correctness of the current approach.

Delay-dependent stability conditions for fundamental characteristic functions

This paper is devoted to the investigation on the stability for two characteristic functions $f_1(z) = z^2+pe^{-z\tau }+q$ and $f_2(z) = z^2+pz e^{-z\tau }+q$, where $p$ and $q$ are real numbers and $\tau >0$. The obtained theorems describe the explicit stability dependence on the changing delay $\tau $. Our results are applied to some special cases of a linear differential system with delay in the diagonal terms and delay-dependent stability conditions are obtained.

Delay-dependent and order-dependent conditions for stability and stabilization of fractional-order memristive neural networks with time-varying delays

The stability and stabilization problems of fractional-order memristive neural networks with time-varying delays are addressed. Based on Jensen-based integral inequalities, novel delay-dependent and order-dependent stability conditions for fractional-order memristive neural networks with time-varying delays are established. The proposed stability criterion is in terms of linear matrix inequalities and is easy to be verified and applied. Then, a linear feedback control law that stabilizes fractional-order memristive neural networks with time-varying delays is designed by utilizing the obtained stability conditions. Two numerical examples are used to illustrate the effectiveness and less conservativeness of the proposed results.

Robust Stability Analysis and Feedback Control for Uncertain Systems With Time-Delay and External Disturbance

This article addresses the delay-dependent Takagi–Sugeno (T–S) fuzzy state feedback control and exponential admissibility analysis for a class of T–S fuzzy singular uncertain systems. First, the T–S fuzzy model is employed to approximate the singular uncertain system with time-varying delay, saturation input, and unmatched disturbance. Second, the delay-dependent T–S fuzzy state feedback controller is designed by employing the T–S fuzzy model. Third, the free-weighting matrices and delay-dependent Lyapunov–Krasovskii functional with multiple integral terms are employed to derive the delay-dependent exponential admissibility conditions and prescribed H-infinity performance is guaranteed. Compared with previous works, the delay-dependent T–S fuzzy state feedback controller is designed for the T–S fuzzy singular uncertain system to relax system design conditions. The convex hull lemma is employed to convert the closed-loop system with saturation input into the closed-loop system without saturation input to enhance controller design flexibility. The Schur complement lemma and Gronwall Bellman lemma are employed to derive the less conservative delay-dependent stability conditions for determining controller gain matrices. The exact invariant set with less conservativeness is employed to convert the controller design problem into linear matrix inequalities (LMIs) optimization constraints to reduce computation complexity of solving LMIs. Finally, simulation examples are presented to show the effectiveness of the proposed methods.

Stability and stabilization of delayed fuzzy systems via a novel quadratic polynomial inequality

The stability and stabilization problems of a class of Takagi-Sugeno(T-S) fuzzy systems with time-varying delay are concerned in this paper. By introducing the tunable parameter l, a novel quadratic polynomial inequality is proposed to reduce the estimation gap with previous work. Sequentially, an appropriate Lyapunov-Krasovskii functional(LKF) containing some new s-dependent integral terms is constructed, the delay-dependent stability condition is further improved by combining the generalized free-matrix-based integral inequality (GFMBII) with the proposed inequality. Finally, four typical numerical examples are carried out to demonstrate the validity and feasibility of the stability criterion and controller design method.

Delay-dependent and order-dependent LMI-based sliding mode [formula omitted] control for variable fractional order uncertain differential systems with time-varying delay and external disturbance

This paper concentrates on the sliding mode H∞ control for variable fractional order uncertain differential systems with time-varying delay and external disturbance by using the delay-dependent and order-dependent LMI approach. Firstly, by designing a suitable variable fractional order sliding mode surface, an equivalent control law has been given and the new state-space model has been introduced. Secondly, by using a Lyapunov–Krasovskii function and constructing an appropriate variable fractional order inequality, a novel delay-dependent and order-dependent stability theorem of the nominal systems without external disturbance is proposed. Then, based on the above stability conditions and the H∞ performance, the delay-dependent and order-dependent stability conditions for the systems with external disturbance are discussed. Moreover, the reachability of the sliding mode surface has been presented. In order to stabilize the systems with uncertainties, the controller gain matrices are also derived with the help of the proposed stability criteria. All the results are in the form of linear matrix inequalities. Finally, two numerical examples are provided to verify the effectiveness of the introduced theoretical formulation.

Delay-Dependent Stability for Load Frequency Control System via Linear Operator Inequality

The stability analysis problem is considered for multiarea load frequency control (LFC) systems with electric vehicles (EVs) and time delays. The novel linear operator inequality approach is proposed and a less conservative delay-dependent stability condition is achieved. First, the model of the multiarea LFC system with EVs and delays is expressed by the partial integral equation (PIE) at the first time. Then, a complete quadratic Lyapunov-Krasovskii functional is built in the form of an inner product of the linear partial integral (PI) operator. The novel stability criteria with less conservatism are proposed in the form of linear operator inequality. Moreover, the relationships between the delay margins and the controller parameters are shown. Finally, the simulations are conducted on both one-area and two-area LFC systems to show the effectiveness of the proposed approach.