Analysis Of Singular Systems Research Articles

State Feedback control of multiagent singular Linear Systems representing brain neural networks

A multi-agent singular system is an extension of a traditional multi-agent system. The behavior of neural networks within the brain is crucial for cognitive functions, making it essential to understand the learning processes and the development of potential disorders. This study utilizes the analysis of singular linear systems representing brain neural networks to delve into the complexities of the human brain. In this context, the digraph approach is a powerful method for unraveling the intricate neural interconnections. Directed graphs, or digraphs, provide an intuitive visual representation of the causal and influential relationships among different neural units, facilitating a detailed analysis of network dynamics. This work explores the use of digraphs in analyzing singular linear multi-agent systems that model brain neural networks, emphasizing their significance and potential in enhancing our understanding of cognition and brain function.

Disturbance rejection analysis of singular time-delay systems based on state decomposition method

The state decomposition technique (SDT) based on memory state-feedback control (MSFC) is used in this article to provide a new disturbance-rejection (DR) method for singular time-delay systems (STSs). First, under MSFC, a singular time-delay control system with disturbance estimator is constructed. Then, a DR control law, which contains disturbance information and MSFC, is designed. Second, the STS is split into algebraic and differential subsystems based on the SDT. Next, a brand-new enhanced Lyapunov–Krasovskii function (LKF) with fewer state vectors is designed. Additionally, a new delay-dependent admissible criterion with fewer decision variables is obtained based on the LKF by combining a Jensen inequality and two zero equations. Third, the controller is designed according to the decomposition component of the controller gain. Finally, the usefulness and efficiency of the strategy are demonstrated by comparing it to a sliding mode control and a traditional control technique.

Wind speed forecasting using Singular Systems Analysis

We report on a method to predict wind speeds up to 24 hours ahead using a technique originating in Dynamical Systems and Chaos theory using a signal processing technique known as Singular Systems Analysis. The method predicts wind speeds based on a set of previous measurements which were used to construct an attractor in an optimally defined phase space as a ‘training set’. Current wind measurements can then be projected to onto that phase space to find most similar previous measurements. By tracing the evolution of these similar previous data, it is possible not only to forecast the wind speed but also to obtain a measure of the expected forecasting uncertainty. The method was applied to a set of hourly wind speed data from a UK Meteorological Office weather station near Edinburgh. A comparison with a simple persistence prediction showed that the Singular Systems Analysis was both, consistently better at predicting wind speeds between 12 and 24 hours ahead than persistence, and also able to provide a meaningful forecasting uncertainty.

On the [formula omitted]-exponential stability of linear positive singular systems with multiple time-varying delays

This paper deals with α-exponential stability analysis of the continuous-time linear positive singular systems with multiple time-varying delays. First, α-exponential stability problem of the single delay case is addressed. For this purpose, delay-range dependent sufficient conditions for such systems, which are regular and impulse-free, are stated in the paper. Then, α-exponential stability conditions for systems with multiple constant delays are addressed, and after that, we extend our idea for stability to multiple delays. To show the usefulness of the proposed conditions, two numerical and practical examples are given.

Finite-time stability analysis of singular neutral systems with time delay

<p>This paper studies the finite-time stability problem for a class of singular neutral systems by using the Lyapunov-Krasovskii function approach and regular neutral system theory. The considered systems involve not only the delayed version of the state, but also the delayed version of the derivative of the state. Some sufficient conditions are presented to ensure that the considered systems are regular, impulse-free, and finite-time stable. Three numerical examples are given to illustrate the effectiveness of the proposed methods.</p>

Discrete-State Decomposition Technique of Dissipativity Analysis for Discrete-Time Singular Systems With Time-Varying Delays.

This article is concerned with the problem of dissipativity for discrete-time singular systems with time-varying delays. First, the discrete-state decomposition technique is proposed after performing the restricted equivalent transformation for singular systems. To reduce the use of decision variables, the state-decomposed Lyapunov function is established based on the decomposed state vectors. Second, to obtain the condition with less conservatism, the two zero-value equations, especially concerning difference subsystems and algebraic ones, the discrete Wirtinger-based inequality and the extended reciprocally convex inequality are employed to bound the forward difference of the Lyapunov function. Then, the less conservative dissipativity criteria with lower computational complexity are obtained. Finally, simulation results are provided to demonstrate the superiority of the proposed technique.

H ∞ performance analysis for 2D discrete singular stochastic systems

This paper addresses the problem of H∞ performance analysis of 2D discrete singular stochastic system described by Roesser model which is challenging since it involves 2D random variables and the disturbance simultaneously. Sufficient conditions are established for the regularity, causality and stability of the system. The proposed results are expressed in terms of strict linear matrix inequalities. Furthermore, a mean square asymptotic stability with an H ∞ disturbance level is developed. Simulation example is provided in order to illustrate the relevance of our approach.

Improved results on admissibility analysis for singular systems with periodically time-varying delay

This paper is concerned with the admissibility analysis for the singular system with a periodically time-varying delay. By dividing the periodic delay interval into monotonically decreasing and increasing intervals, a novel Lyapunov–Krasovskii functional (LKF) is developed in virtue of the looped functional philosophy, relaxing the positive definition of the LKF and making full use of the system state and the time-varying delay function information. Then, a new admissibility condition is derived by combining the newly constructed LKF and the second-order canonical Bessel–Legendre integral inequality. Finally, two numerical examples are given to demonstrate the superiority of the developed method.

Reduced-Complexity LMI Conditions for Admissibility Analysis and Control Design of Singular Nonlinear Systems

We present a reduced-complexity control approach for a class of descriptor nonlinear systems with a nonlinear derivative matrix, possibly singular. To this end, a systematic approach is proposed to obtain an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">equivalent</i> polytopic representation of a given nonlinear system within a compact set of the state-space. This modeling approach has two particular features compared to the related Takagi–Sugeno (T–S) fuzzy model-based framework. First, the model complexity only grows <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">proportionally</i> , rather than exponentially, with the number of premise variables. Second, the vertices of the proposed polytopic models can admit an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infinite</i> number of representations for the same predefined set of premise variables. This <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nonuniqueness</i> feature allows introducing some specific slack variables at the modeling step to reduce the control design conservatism. Based on the proposed polytopic representation and Lyapunov stability theory, we derive reduced-complexity admissibility analysis and design conditions, expressed in terms of linear matrix inequalities, for the considered class of descriptor systems. In particular, a new nonlinear control law is proposed for regular descriptor systems to avoid using the extended redundancy form, which may yield numerically complex and conservative results due to the imposed special control structure. Both numerical and physically motivated examples are given to demonstrate the interests of the new control approach with respect to existing T–S fuzzy model-based control results.

Admissibility Analysis and Control for Discrete-Time Singular Systems with Interval Time-Varying Delay

This paper mainly investigates an admissibility analysis and controller design problem for an uncertain discrete-time singular system with delayed states. The time-varying delay is within an interval whose lower bound may be greater than zero. Using a modified finite sum inequality and choosing a suitable Lyapunov-Krasovskii function, we derive a set of LMI-based sufficient delay-dependent conditions for the admissibility analysis and controller synthesis problem, respectively. In the end, a numerical example shows the effectiveness and validity of the proposed approach.

On Stability Analysis of Riemann-Liouville Fractional Singular Systems with Delays

In this study, two lagged fractional order singular neutral differential equations are considered. Using the advantage of the association property of the Riemann -Liouville derivative, the derivative of the appropriate Lyapunov function is calculated. Then, with the help of LMI, sufficient conditions for asymptotic stability of zero solutions are obtained.

Stability analysis of nonlinear time-delay singular systems via improved barbălat’s lemma

This paper revisits asymptotic stability problem of nonlinear time-delay singular systems (NTDSs). Many existing stability results for this problem are derived based on the classical Barbălat’s lemma. This lemma puts two requirements on the considered functions or functionals. One is uniform continuity, the other is boundedness of the infinite integral. However, in some cases, the first requirement is difficult to be satisfied. To mitigate this limitation, a novel improved Barbălat’s lemma is proposed in some literature. In this improved lemma, the requirement of uniform continuity is relaxed by quasi-uniform continuity. By virtue of this improved Barbălat’s lemma, this paper establishes a less conservative stability theorem for NTDSs. Then, the derived results related to NTDSs are applied to investigate stability problem of linear time-delay singular systems. To demonstrate the effectiveness of the proposed results, a numerical example about circuit systems is provided.

New Admissibility and Admissibilization Criteria for Nonlinear Discrete-Time Singular Systems by Switched Fuzzy Models

Admissibility analysis and control synthesis for nonlinear discrete-time singular systems are considered in this article. With regard to the type-1 and interval type-2 fuzzy singular systems, the partition of membership functions and scale transform is imposed, and new switched fuzzy systems, which are equivalent to the original systems, are established. A relaxed stability criterion is derived to ensure the admissibility of the system by using the piecewise Lyapunov function and singular value decomposition. Moreover, two classes of switched controllers are designed for the systems. One is for type 1 systems and the membership functions are consistent with those of the systems. The other can be applied to both of the fuzzy systems by introducing linear membership functions in each subregion. Two criteria are obtained to guarantee that the closed-loop systems are admissible. Several illustrative examples are provided to show the effectiveness of the developed methods.

Further Improvement for Admissibility Analysis of Singular Time-Delay Systems

This article concerns the admissibility analysis of singular time-delay systems. The aim is to get superior criteria in both low conservativeness and less decision variables. To this end, the systems are decomposed and treated with different methods. The Lyapunov–Krasovskii functionals (LKFs) are constructed based on the state decomposition. By using tighter integral inequalities and the free weighting matrix method, some new admissibility criteria are derived to compare with the previous results, and are applied to the partial element equivalent circuits (PEECs) in numerical examples, by which the advantages of the proposed method are verified.

Introduction to fractional analysis of singular («rigid») systems of differential equations representing material objects of railway transport

Introduction to fractional analysis of singular («rigid») systems of differential equations representing material objects of railway transport

Formation tracking for singular swarm systems subjected to energy constraints and switching transmission topologies

AbstractThis article investigates admissible formation tracking for singular swarm systems under conditions of switching transmission topologies as well as the limited energy supply, where both switching transmission topologies containing a spanning tree and switching transmission topologies containing a joint spanning tree are addressed. First, a new formation control tracking protocol with switching transmission topologies is proposed to realize admissible formation tracking, where the total energy supply is predetermined. Afterwards, by a dual nonsingular transformation, the disagreement dynamics between followers and the leader is determined and the impacts of asymmetric structures of switching transmission topologies are eliminated. Sufficient conditions for admissible formation tracking design and analysis for singular swarm systems with switching transmission topologies containing a spanning tree and with switching transmission topologies containing a joint spanning tree are proposed, respectively, where the coupling relationship matrix between the total energy supply and the matrix variable is determined. Finally, two numerical simulations are presented to demonstrate the effectiveness of theoretical results.

New insight into admissibility analysis for singular systems with time-varying delays

This paper focuses on the admissibility analysis of singular systems with time-varying delays. The goal is to obtain admissibility criterion with less conservatism and fewer decision variables. After decomposing singular systems into differential subsystems and algebraic ones, an improved augmented Lyapunov–Krasovskii functional is established according to decomposed state vectors. Then, combining the auxiliary function-based inequality and the extended reciprocally convex matrix method, a less conservative admissibility criterion with fewer decision variables is obtained. Finally, a numerical example verifies the reduced conservatism and calculation burden of the presented method.

Observer-based proportional derivative fuzzy control for singular Takagi-Sugeno fuzzy systems

This study investigates the issue of stability analysis and controller synthesis for nonlinear singular systems . Via applying a fuzzy modeling approach, the nonlinear singular system is expressed by a Takagi-Sugeno (T-S) fuzzy model composed of several linear subsystems. Furthermore, the parallel distributed compensation fuzzy controller is designed such that the controlled singular system is stable. Employing Proportional Derivative (PD) control method, the regularity and impulse-free property of the singular systems can be held. However, the PD control method is challengable because the state signals of singular systems are not always measurable. Therefore, a novel fuzzy observer is designed to ensure the existence of estimated states. For the observer-based PD control issue, some sufficient stability conditions are derived for T-S fuzzy singular systems. Moreover, the control gains and observer gains can be conveniently calculated using the Linear Matrix Inequality (LMI) calculation. Finally, two numerical examples are presented to verify the availability and applicability of the proposed design method.

State bounding and L ∞-gain for positive singular systems with unbounded time-variable delay

This paper studies the problems of state bounding and -gain analysis for positive singular systems with unbounded time-variable delays and bounded disturbance for the first time. By a novel approach, we derive componentwise state bounds for positive singular system with or without bounded disturbances. An application to -gain problem of positive singular systems with unbounded time-variable delays is also presented. A numerical example is conducted to validate the effectiveness of our results.

Stability analysis of singular time-delay systems using the auxiliary function-based double integral inequalities

Recently, there have been a few developments reported on using the Wirtinger/free-matrix-based single integral inequality to stability problem of singular time-delay systems but there has been no report on the double ones. This paper presents an extension on applying the auxiliary function-based double integral inequality to the problem. Furthermore, an extension of the delay-dependent matrix technique into the single integral term of the Lyapunov–Krasovskii function to reduce more the conservatism has also been presented. By proposing an extended Lyapunov–Krasovskii functional (LKF) with triple integral terms and three delay-dependent matrices, a new delay-derivative-dependent stability criterion is derived. The effectiveness of the obtained result is illustrated through a numerical example.