Delay-dependent Stability Research Articles

Delay-Dependent Stability Improvement for Networked Control Systems: a Sampled Data Approach

This paper concerns the stability conditions and controller design for sampled-data networked control systems (NCSs) model subject to network communication delays, the main objective is to guarantee the maximum allowable upper bounds of network-induced time-varying delays that keep the NCSs stable. First, Lyapunov-Krasovskii functional with simple and double-integral terms is constructed considering both upper and lower bounds of network delay. Then, less conservative Linear Matrix Inequalities (LMIs) stability conditions are established using null terms to introduce free weighting matrices based on the Leibniz-Newton formula. Furthermore, Finsler's lemma is used for the relaxation of the obtained LMI's stability conditions using slack decision variables. It is also used to decouple Lyapunov-Krasovskii matrices from the system ones. The application of the proposed approach for different NCSs gives higher upper delay bounds compared with other methods.

Stability Analysis and Controller Design of Networked Active Vehicle Suspension System Subject to Delays and Packet Losses

In this paper, the stability analysis and control design of networked control systems (NCS) subject to network induced delay and packet dropouts, the study is aiming to maximize the allowable upper bound of network induced delay together with the number of consecutive packet dropouts, The analysis method utilizes a new Lyapunov-Krasovskii (LKF) functional to provide less conservative results. The delay-dependent stability criteria based on improved Wirtinger inequality and reciprocally convex combination inequality are derived in terms of linear matrix inequalities (LMI). Finally, numerical examples are given to show the effectiveness of the proposed analysis method compared to other existing methods.

Distributed Double-Layer Control for Coordination of Multiplatoons Approaching Road Restriction in the Presence of IoV Communication Delays

Internet of Vehicle (IoV) has become a hot topic in the last years due to its significant benefits in transportation systems in terms of quality, costs, and traffic management capability. Indeed, accurate and real-time information acquisition and diffusion are required to reach an efficient traffic management system according to the smart city paradigm. In this context, this article provides a novel IoV-based distributed double layer control architecture to address the coordination control problem of connected autonomous vehicles (CAVs) multiple platoons negotiating the access to a road section restriction in the presence of heterogeneous communication time-varying delays. To this aim, leveraging the IoV paradigm and the equivalent virtual formation concept, we propose a novel distributed diffusive longitudinal protocol and a distributed lateral potential-function-based control strategy, where both of them are able to cope with communication delays and ensuring the multiplatoon coordination in finite time, i.e., before accessing the road section restrictions, so to avoid vehicles collisions. The finite-time stability of both the cooperative controllers is analytically proved by exploiting the Lyapunov–Krasovskii theory and the derived delay-dependent stability conditions, expressed as a set of linear matrix inequalities (LMIs), allows the proper tuning of the controllers gains. Numerical analysis confirms the theoretical derivation and discloses the effectiveness and the robustness of the proposed cooperative multiplatoon control in ensuring the safe crossing of the road section restriction in finite time.

LMIs-based stability analysis and fuzzy-logic controller design for networked systems with sector nonlinearities: Application in tunnel diode circuit

In this article, the problem of exponential mean-square stability analysis is discussed for uncertain networked control systems expressed by a stochastic T-S fuzzy model. In general, the characteristics of random occurrence for multipath packet dropouts often exist in the signal transmission network. For dealing with this difficult point, a dynamic output feedback strategy combining stochastic Bernoulli theory is employed. Then, delay-dependent stability conditions are derived and closed-loop system is exponentially mean-square stable by designing fuzzy-basis-dependent Lyapunov functional. Furthermore, in terms of linear matrix inequalities (LMIs) technology, sufficient conditions are gained to guarantee the prescribed H-infinity performance. Different from previous literatures, the congruence transformation method is employed to determine controller gain matrices for reducing the computation complexity of solving LMIs. Finally, the proposed method is applied in tunnel diode circuit model to verify the applicability.

Global exponential stability of memristor based uncertain neural networks with time-varying delays via Lagrange sense

ABSTRACT This paper addresses the global exponential stability in Lagrange sense for memristor-based neural networks (MNNs) with time-varying delays. This paper attempts to derive the delay-dependent Lagrange stability conditions in terms of linear matrix inequalities by designing a suitable Lyapunov-Krasovskii functionaland used Wirtinger inequality, Jensen-based inequality for estimating the integral inequalities. The conditions which are derived confirms the globally exponential stability in Lagrange sense for the proposed MNNs and, the detailed estimation for global exponential attractive set is also given. To show the effectiveness and applicability of the proposed criteria, two numerical examples are also provided in this paper.

Stability analysis of delayed neural network based on the convex method and the non-convex method

This paper investigates the asymptotic stability of neural network with time-varying delay. A new Lyapunov–Krasovskii functional (LKF) is constructed with some non-integral delay-product functional terms. Some parameter matrices in the LKF are not required to be positive definite. The convex method and the non-convex method are proposed to deal with the square of the time-varying delay appearing in the derivative of the LKF, respectively. Two less conservative delay-dependent stability criteria in the form of linear matrix inequalities (LMIs) are established. Finally, two widely used numerical examples are given to illustrate the validity and superiority of the obtained stability criteria.

Improved Fixed-Time Stability Lemma of Discontinuous System and its Application

As is known to all that the Lyapunov-Krasovskii functional (LKF) has played a vital role in studying the fixed-time (FXT) stability of the time-delayed Filippov discontinuous systems. When investigating the FXT stability of the time-delayed discontinuous systems, the interesting topic is to provide the more relaxed conditions imposed on the LKF and obtain the more accurate settling-time (ST). This paper aims to investigate the new FXT stability lemma with more relaxed conditions for the time-delayed Filippov discontinuous systems. By using some novel inequality techniques and analytical methods, the new FXT stability lemma is established and more accurate ST is estimated. The traditional discussion about <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0 &lt; V &lt; 1$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V \geq 1$ </tex-math></inline-formula> is not required. For the purpose of validation, FXT stabilization of discontinuous inertial networks with mixed time delays is considered. By using differential inclusions theory and the new FXT stability lemma, the delay-dependent FXT stabilization criteria are derived. It is the first time to derive the delay-dependent FXT stabilization criteria for the discontinuous inertial networks. Finally, examples are given to show the effectiveness of the established results.

Delay-dependent Stability Criteria for Linear Systems with Two Additive Time-varying Delays

Delay-dependent Stability Criteria for Linear Systems with Two Additive Time-varying Delays

Finite-region stability of 2-D singular Roesser systems with directional delays

In this paper, the problem of finite-region stability is studied for a class of two-dimensional (2-D) singular systems described by using the Roesser model with directional delays. Based on the regularity, we first decompose the underlying singular 2-D systems into fast and slow subsystems corresponding to dynamic and algebraic parts. Then, with the Lyapunov-like 2-D functional method, we construct a weighted 2-D functional candidate and utilize zero-type free matrix equations to derive delay-dependent stability conditions in terms of linear matrix inequalities (LMIs). More specifically, the derived conditions ensure that all state trajectories of the system do not exceed a prescribed threshold over a pre-specified finite region of time for any initial state sequences when energy-norms of dynamic parts do not exceed given bounds.

An improved stability criterion for discrete-time time-delayed Lur'e system with sector-bounded nonlinearities

The absolute stability problem of discrete-time time-delayed Lur'e systems with sector bounded nonlinearities is investigated in this paper. Firstly, a modified Lyapunov-Krasovskii functional (LKF) is designed with augmenting additional double summation terms, which complements more coupling information between the delay intervals and other system state variables than some previous LKFs. Secondly, some improved delay-dependent absolute stability criteria based on linear matrix inequality form (LMI) are proposed via the modified LKF and the relaxed free-matrix-based summation inequality technique application. The stability criteria are less conservative than some results previously proposed. The reduction of the conservatism mainly relies on the full use of the relaxed summation inequality technique based on the modified LKF. Finally, two common numerical examples are presented to show the effectiveness of the proposed approach.

Delay-dependent input-output stability conditions for non-autonomous neutral type differential equations in a Banach space

In a Banach space we consider a class of linear non-autonomous neutral type differential equations with several delays. For the considered equations we derive explicit delay-dependent input-output stability conditions. Applications to neutral type integro-differential equations are also discussed.

Delay-Dependent Positivity and Stability Analysis of Discrete-Time Systems With Delay

In this letter, delay-dependent positivity and stability conditions, which are crucially different from existing delay-independent ones, are derived for discrete-time systems with time-varying delay. By utilizing a special property called non-oscillatory behavior of solutions of scalar difference equations with delays, the proposed conditions are formulated in terms of linear programming settings. The efficiency of the obtained results is illustrated by a numerical example with simulations.

An Improved Stability Criterion for Discrete-Time Linear Systems With Two Additive Time-Varying Delays

In this paper, the stability analysis problem for discrete-time linear systems with additive time-varying delays is further investigated. In the first place, an augmented Lyapunov-Krasovskii functional (LKF) based on delay interval decomposition is designed, where some augmented vectors are selected to supplement the coupling relationships between some system state variables and different delay subintervals. In the second place, based on the augmented LKF, a new delay-dependent stability criterion is derived vai a general summation inequality lemma. The stability criterion is derived in the form of linear matrix inequality (LMI), which can be solved quickly by Matlab LMI-Tool. In the end, the effectiveness of the proposed method is illustrated by some common numerical examples.

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

This paper 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. Firstly, the T-S fuzzy model is employed to approximate the singular uncertain system with time-varying delay, saturation input and unmatched disturbance. Secondly, the delay-dependent T-S fuzzy state feedback controller is designed by employing the T-S fuzzy model. Thirdly, 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.

Improved Delay-Dependent Stability Analysis of Fixed-Point State-Space Digital Filters With Time-Varying Delay and Generalized Overflow Arithmetic

This paper is concerned with the stability analysis of fixed-point state-space digital filters with generalized overflow arithmetic and a time-varying delay. This paper aims to derive a delay and nonlinear function bound dependent asymptotical stability criterion with less conservatism. Firstly, a new Lyapunov functional with several augmented terms, including extra free matrices and overflow nonlinear function, is constructed such that it has a relaxed positive condition. Then, for bounding the summation term arising in the forward difference of Lyapunov functional, a new lemma is developed to introduce the terms for linking the delayed states and the overflow nonlinear function, the Wirtinger-based summation inequality and several zero-value terms are applied to add more cross terms. As a result, a stability criterion with less conservatism is established and its conservatism. Finally, several numerical examples are given to illustrate the advantages of the proposed method.

Impact of Time Delay Margin on the Stability of Load Frequency Systems with Electric Vehicle Aggregator

Open channel communication is a major prerequisite for next generation power networks in which time delays are inevitable. Due to unforeseen variations in the load demand, the mismatch between power generation and demand occurs. If this situation is not properly tackled, it may induce some unintended consequences like fluctuations in the tie-line power and system frequency which are highly undesirable. To ensure grid reliability, the frequency should always stay within its stipulated range. This is accomplished by load frequency control (LFC) technique. In networked LFC systems, load frequency regulation signals are transferred via communication networks, causing time delays in the feedback paths that can destabilize the power grid. As a consequence, for ensuring stability, the stable delay margin must, therefore, be determined. In this paper, the delay-dependent stability problem of two area LFC systems combined with electric vehicle aggregator (EVA) is addressed. The conducted Lyapunov based analysis yields a stable delay margin within which the closed loop system remains asymptotically stable. Moreover, the analytical delay margin values are validated using the simulation studies. In the sequel, the effect of participating factors on the system stability is also investigated.

Stability Analysis of Time-Delay Systems via a Delay-Derivative-Partitioning Approach

This paper is devoted to the study of delay-dependent stability of time-varying delay systems. A delay-derivative-partitioning approach is proposed. By constructing an augmented Lyapunov functional that contains two delay-product-dependent terms and using the delay-derivative-partitioning approach, an improved stability condition is established. The derived condition is described as a set of linear matrix inequalities, which can be readily implemented. Finally, four examples are carried out so as to attest the effect and merit of the presented approach.

Stabilization of Fuzzy Hydraulic Turbine Governing System With Parametric Uncertainty and Membership Function Dependent H∞ Performance

This paper examines the stabilization problem and membership function dependent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> performance analysis for uncertain hydraulic turbine governing systems with stochastic actuator faults and time-varying delays via sampled-data control. At first, the nonlinear hydraulic turbine systems are modeled as Takagi-Sugeno (T-S) fuzzy systems with time-varying delay and bounded external disturbance through membership functions. Then, a novel delay-dependent looped Lyapunov-Krasovskii functional (LKF) is formulated with complete information throughout the sampling interval. In the meantime, a membership function dependent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> performance index is suggested to diminish the impact of disturbances on the uncertain fuzzy system. Based on the robust control and novel LKF, new delay-dependent stability conditions for the closed-loop system are attained in the framework of linear matrix inequalities (LMIs). At last, the numerical example validates the proposed theoretical contributions in terms of achieving robust stability and minimizing disturbance attenuation levels.

Delay margin computation of load frequency control system with demand response and constant communication delays

The paper aims to present a comprehensive delay-dependent stability analysis technique of a networked single area Load Frequency Control (LFC) systems integrated with demand response. Demand Response (DR) has been an integral part of power system control and operation. The time-delays in LFC schemes are due to the utilization of communication channels for signal transmission among the various sub-systems and control center. The deterioration of the dynamic performance of the system is the most feasible effect of time-delays and at the worst these delays lead to instability. Therefore, the computation of delay margins for a stable operation of the single-area LFC system with DR control is crucial. A less conservative stability criterion using Lyapunov approach is derived in linear matrix inequality framework for determining the stability of closed loop LFC system under study. The stability criterion is tested for different subsets of the controller parameters and participation factors using standard benchmark system. Through extensive simulation results, the analytical results are validated. The time domain simulation results indicate the effectiveness of the analytical results.

Delay-dependent stability of high-order neutral systems

Delay-dependent stability of high-order neutral systems