LMI-based Stability Conditions Research Articles

Suppression of Packet Losses and Disturbances in Networked Control Systems Based on Equivalent-Input-Disturbance Approach.

This article presents a method of suppressing packet losses and exogenous disturbances for a networked control system (NCS) subject to network-introduced delays. The NCS has two feedback loops: 1) a local one and 2) a main one. The local feedback loop contains a state observer, an equivalent-input-disturbance (EID) estimator, and state feedback. It is used to ensure prompt disturbance suppression. The controller in the main feedback loop contains an internal model to track a reference input. The system is divided into two subsystems for the design of controllers. The state-observer gain is designed for one subsystem using the concept of perfect regulation to ensure disturbance estimation performance. The state-feedback gains of the other subsystem are designed based on a stability condition in the form of a linear matrix inequality (LMI). A tracking specification is embedded in the LMI-based stability condition to ensure satisfactory tracking performance. A case study on a two-finger robot hand control system and a comparison with a Smith-EID and H∞ controller approach validate the effectiveness and superiority of the presented method.

Delay partitioning approach to the delay-dependent stability of discrete-time systems with anti-windup

ABSTRACT In this digital era, the basis of every smart instrument is discrete signal models e.g. in Networked control systems, Cyber physical systems etc. It has been shown that time-delays are unavoidable during the digital implementation of an engineering system. Therefore, the stabilization of discrete time delayed systems is gaining the high importance [1–10]. Although a lot of literature is found on the stabilization of time delayed systems for a long time using the construction of proper non-negative Lyapunov functional. Recalling some existing results on this issue, the LMI-based stability conditions are obtained by its forward difference negative-definite in direction to claim the less conservative results [15–25]. In order to seek less conservative stability criteria, this paper introduces an anti-windup scheme appended with Wirtinger inequality, reciprocal convex approach and delay partitioning of a discrete-time delayed systems by using Lyapunov Krasovskii functional. To accomplish this task, delay partitioning technique may be utilized to develop improved stability conditions for the considered system. The Wirtinger-based inequality and reciprocal convex approach has been employed to derive less conservative results. On employing the delay partitioning, a novel linear matrix inequality-based criterion is proposed to stabilize such systems. The considered Lyapunov-Krasovskii functional includes the information of intermediate delay to acknowledge the delay information implicitly that ensures the considered system to be regular, impulse free and stable in terms of linear matrix inequalities. The estimation of the attraction basin is to ensure that the state remains inside the level set of a certain Lyapunov function. Numerical simulation verifies that the presented method reduces conservatism than the existing results.

LMI-Based Stability Conditions for Continuous Fractional-Order Two-Dimensional Fornasini-Marchesini First Model

In this brief, the structural stability of continuous fractional-order (FO) two-dimensional (2D) Fornasini-Marchesini (FM) first model is investigated. Firstly, the bivariate polynomial-based stability condition is equivalently transformed to be in more tractable form. Then, based on generalized KYP lemma, the transformed conditions are further reduced into the feasibility problem of linear matrix inequalities (LMIs). The main contribution is to establish the LMI-based stability conditions for continuous FO 2D FM first model. The results can be applied in the cases with FO <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha _{i} \in (0,2)$ </tex-math></inline-formula> and be no conservative when the FO in the second dimension <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha _{2} \in [1,2$ </tex-math></inline-formula> ). Lastly, the example is provided to verify the efficiency.

Reset Control for Consensus of Multiagent Systems With Asynchronous Sampling

This article investigates the consensus problem of multiagent systems (MASs) with the reset control approach. Reset control has been shown to possess great potential to improve transient system performance, but reset-induced state jump dynamics bring difficulties for consensus analysis, especially under the network environment. In this article, a novel reset element is developed, and time regularization is utilized to exclude Zeno behavior. The case with continuous communication is first considered, a distributed proportional integral + reset consensus protocol is proposed, which consists of the proportional-integral controller and the reset mechanism. The results are further generalized to the case with asynchronous sampling, which relaxes the requirement for continuous communication and clock synchronization. A hybrid model of the MAS is constructed to describe the system dynamics, and a hybrid systems approach is proposed to handle the reset- and sampling-induced jump dynamics in a unified framework. Moreover, a novel Lyapunov function is proposed and LMI-based stability conditions are given. Finally, an example is provided to show the effectiveness of the proposed methods.

Asynchronous [formula omitted] observer-based control synthesis of nonhomogeneous Markovian jump systems with generalized incomplete transition rates

This paper deals with the problem of asynchronous H∞ observer-based control for continuous-time nonhomogeneous Markovian jump systems with generalized incomplete transition rates. Different from other existing papers, the effects of both nonhomogeneity and asynchronism on observer-based control design are discussed in detail to address more realistic phenomena. Furthermore, to decouple the Lyapunov matrix from the control gain while improving the control performance, this paper proposes a state extension method as an alternative to the conventional separation method. Not only that, to derive a set of LMI-based stabilization conditions, this paper presents a less conservative relaxation technique that reduces its computational burden. Finally, two illustrative examples are provided to show the validity of the proposed method.

Improved robust H ∞ stability analysis and stabilisation of uncertain and disturbed networked control systems with network-induced delay and packets dropout

This paper is concerned with stability analysis and stabilisation of uncertain Networked Control Systems (NCS) with network-induced delay and packet dropouts. This proposal aims at maximising the allowable upper bound of network-induced delay, together with the number of consecutive packet dropouts, from which uncertain and disturbed NCS plants are stable. A novel augmented Lyapunov–Krasovskii functionals (LKF), dependent on both the lower and upper bounds of the network-induced time-varying delay, is considered to derive the proposed delay-dependent LMI-based stability conditions. Relaxation of these conditions are obtained by exploiting simple and double integral Wirtinger's inequalities to introduce more degrees of freedom from the LKF terms than existing related conditions in the literature. Finally, numerical examples and simulation results are presented to illustrate the effectiveness and the conservatism improvement raised by this proposal compared to previous related results.

H ∞ fault detection for 2-D T–S discrete stochastic fuzzy systems

ABSTRACT This paper is concerned with fault detection (FD) problem for a class of two-dimensional (2-D) Takagi–Sugeno (T–S) discrete stochastic fuzzy systems. Based on the parallel distributed compensation (PDC), the fuzzy FD filter and the dynamics of FD system are constructed. Since the multiplicative property of the FD system would drastically increase the number of the stability conditions, a method of decoupling based on dimension expansion is used. By decoupling, the number of LMI-based stability conditions is reduced to r from by the conventional method. Then, the fuzzy FD filter is designed. The corresponding fuzzy FD system is proved to be mean-square asymptotically stable and satisfies the attenuation level for all disturbances. In addition, a theorem is proposed to prove that the stability conditions based on decoupling method are equivalent to those of conventional method. Finally, simulation examples are provided to demonstrate the usefulness of the proposed design methods.

Extended state observer-based control for systems with locally Lipschitz uncertainties: LMI-based stability conditions

This paper deals with the closed-loop stability of an extended state observer-based control for systems with locally Lipschitz uncertainties. Novel stability conditions are developed, in terms of Linear Matrix Inequalities (LMI), in order to prove its local/global input-to-state or exponential stability, respectively. The stability conditions of this paper do not require neither the uncertainty to satisfy the so-called matched condition, nor the system to be expressed in the canonical integral chain form. LMI-based optimization methodologies are also developed in order to optimize the presented results.

Improved LMI-based stability conditions for a competitive Lotka\u2013Volterra system with time-varying delays

This paper is concerned with the local asymptotic stability problem for a competitive Lotka–Volterra system with time-varying delays. By constructing the novel augmented Lyapunov–Krasovskii functionals and using the Wirtinger integral inequality, some alternative stability criteria are obtained by means of linear matrix inequalities. In particular, our constructed functionals contain some cross terms related to four different time delays. The proposed stability conditions in this paper are less conservative as compared with the most existing ones due to using some advanced techniques. Finally, a numerical example illustrates the effectiveness and improvement of the obtained results.

An improved time-delay implementation of derivative-dependent feedback

We consider an LTI system of relative degree r≥2 that can be stabilized using r−1 output derivatives. The derivatives are approximated by finite differences leading to a time-delayed feedback. We present a new method of designing and analyzing such feedback under continuous-time and sampled measurements. This method admits essentially larger time-delay/sampling period compared to the existing results and, for the first time, allows to use consecutively sampled measurements in the sampled-data case. The main idea is to present the difference between the derivative and its approximation in a convenient integral form. The kernel of this integral is hard to express explicitly but we show that it satisfies certain properties. These properties are employed to construct the Lyapunov–Krasovskii functional that leads to LMI-based stability conditions. If the derivative-dependent control exponentially stabilizes the system, then its time-delayed approximation stabilizes the system with the same decay rate provided the time-delay (for continuous-time measurements) or the sampling period (for sampled measurements) are small enough.

State and unknown inputs estimation for Takagi–Sugeno systems with immeasurable premise variables: Proportional Multiple Integral observer design

In this work, we focus on the design of a Proportional Multiple Integral (PMI) observer for Takagi–Sugeno (T–S) fuzzy systems with immeasurable premise variables subjected to unknown inputs. The LMI-based stability conditions are significantly relaxed by the introduction of an output error injection in the premise variable of the PMI observer. The efficiency of the proposed observer is finally illustrated by a simulation example of a chaotic system.

Discrete-time stochastic impulsive BAM neural networks with leakage and mixed time delays: An exponential stability problem

In this paper, the stability analysis of impulsive discrete-time stochastic BAM neural networks with leakage and mixed time delays is investigated via some novel Lyapunov–Krasoviskii functional terms and effective techniques. For the target model, stochastic disturbances are described by Brownian motion. Then the result is further extended to address the problem of robust stability of uncertain discrete-time BAM neural networks. The conditions obtained here are expressed in terms of Linear Matrix Inequalities (LMIs), which can be easily checked by MATLAB LMI control toolbox. Finally, few numerical examples are presented to substantiate the effectiveness of the derived LMI-based stability conditions.

Fuzzy Static Output Feedback H∞ Control for Nonlinear Systems Subject to Parameter Uncertainties

This study is concerned with the stabilization issue of nonlinear systems subject to parameter uncertainties. An interval type-2 T-S fuzzy model is used to represent the nonlinear systems subject to parameter uncertainties. An interval type-2 fuzzy static output feedback controller is designed to synthesize the interval type-2 T-S fuzzy systems. The membership-function-dependent stability conditions are derived by utilizing the information of upper and lower membership functions. The proposed stability conditions are presented in the form of linear matrix inequalities (LMIs). LMI-based stability conditions for interval type-2 fuzzy static output feedback H∞ control synthesis are also developed. Several simulation examples are given to show the superiority of the proposed approach.

Stability analysis of reaction-diffusion uncertain memristive neural networks with time-varying delays and leakage term

In this paper, the stability problem is investigated for a class of reaction-diffusion uncertain memristive neural networks with time-varying delays and leakage term. To investigate the dynamic behavior of the memristive system, we turn to the qualitative analysis of a relevant differential inclusion under the framework of Filippov’s solution, which is easier to handle. By using Lyapunov stability theory, Jensen integral inequality, Schur complement Lemma, free-weighting matrix approach together with the linear matrix inequality (LMI) approach, the sufficient conditions are derived to ensure the stability of the considered systems. The easy-to-test stability criteria established in this paper depend on the leakage delay as well as the reaction-diffusion terms, which is more reasonable. Moreover, the existing stability criteria can be treated as a special case of this paper. Finally, two numerical examples are exploited to show the effectiveness of the derived LMI-based stability conditions.

Design of exponential state estimators for neutral-type neural networks with mixed time delays

In this paper, the state estimation problem is dealt with for a class of neutral-type neural networks with mixed time delays. We aim at designing a state estimator to estimate the neuron states, through available output measurements, such that the dynamics of the estimation error is globally exponentially stable in the presence of mixed time delays. By using the Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions to guarantee the existence of the state estimators. A simulation example is exploited to show the usefulness of the derived LMI-based stability conditions.

An efficient approach for reducing the conservatism of LMI-based stability conditions for continuous-time T–S fuzzy systems

This paper deals with reducing the conservatism of stability conditions for continuous-time T–S fuzzy systems. Previous stability conditions are relaxed by further exploring the properties of the time derivatives of normalized fuzzy weighting functions and by introducing more slack matrix variables. By relying on analysis of the positive and negative characteristics of the time derivatives of normalized fuzzy weighting functions, some redundant terms are removed from the problem formulation. Furthermore, more slack matrix variables are introduced to enlarge the design space. Consequently, less conservative stability conditions are obtained. Finally, a well-known numerical example is provided to illustrate the effectiveness of the proposed result.

Linear matrix inequalities‐based membership‐function‐dependent stability analysis for non‐parallel distributed compensation fuzzy‐model‐based control systems

This study investigates the stability of fuzzy-model-based (FMB) control system, which is formed by a Takagi–Sugeno (T–S) fuzzy model representing a non-linear plant and a fuzzy controller connected in a closed loop. The proposed fuzzy controller considers a higher design flexibility that the premise membership functions and the number of fuzzy rules are allowed to be not the same as those of the T–S fuzzy model. By employing simple membership functions and a smaller number of fuzzy rules, the complexity of the fuzzy controller can be reduced to facilitate its implementation. Based on the Lyapunov stability theory, a membership-function-dependent (MFD) stability analysis is proposed to develop stability conditions in the form of linear matrix inequalities (LMIs) to determine the system stability and facilitate the control synthesis. The information of the membership functions is brought to the MFD LMI-based stability conditions, which are dedicated to the FMB control system under consideration. It is thus the proposed MFD stability analysis result is more relaxed compared with the existing membership-function-independent stability analysis results. A simulation example is given to illustrate the effectiveness of the proposed approach.

Stability analysis of nonlinear-function fuzzy-model-based control systems

This paper presents the stability analysis of nonlinear-function fuzzy-model-based (FMB) control systems. A fuzzy model with nonlinear function terms is proposed to represent nonlinear plants. A fuzzy controller with the nonlinear function terms is then proposed to close the feedback loop. The nonlinear function terms enhance the capability of fuzzy modelling and feedback compensation. Following the linear-matrix-inequality (LMI) based stability analysis approach for the traditional FMB control systems, it will lead to stability conditions involving the nonlinear terms for the proposed nonlinear-function FMB control systems. As a result, the stability conditions will have an infinite number of LMIs, which make it impractical to find a feasible solution numerically using convex programming techniques. A stability analysis approach is proposed to obtain effective LMI-based stability conditions for the proposed nonlinear-function FMB control systems. Simulation examples are given to illustrate the merits of the proposed fuzzy control approach.

Improved Delay-Dependent Robust Stability Criteria for Discrete-Time Stochastic Uncertain Networks with Time-Varying Delays

In this paper, the mean square asymptotical stability is investigated for a class of discrete-time stochastic systems with time-varying delays and norm-bounded uncertainties,a numerical example is presented to show the usefulness of the derived LMI-based stability condition.

Exponential stability for stochastic BAM networks with discrete and distributed delays

In this paper, we investigate exponential stability for stochastic BAM networks with mixed delays. The mixed delays include discrete and distributed time-delays. The purpose of this paper is to establish some criteria to ensure the delayed stochastic BAM neural networks are exponential stable in the mean square. A sufficient condition is established by consructing suitable Lyapunov functionals. The condition is expressed in terms of the feasibility to a couple LMIs. Therefore, the exponential stability of the stochastic BAM networks with discrete and distributed delays can be easily checked by using the numerically efficient Matlab LMI toobox. A simple example is given to demonstrate the usefulness of the derived LMI-based stability conditions.