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Geophysicists have studied three-dimensional quasi-geostrophic systems extensively. These systems describe stratified flows in the atmosphere on a large timescale and are widely used for forecasting atmospheric circulation. They couple an inviscid transport equation in R+×Ω with an equation on the boundary satisfied by the trace, where Ω is either a two-dimensional torus or a bounded convex domain in R². In this paper, we show the existence of global in time weak solutions to a family of singular three-dimensional quasi-geostrophic systems with Ekman pumping, where the background density profile degenerates at the boundary. The proof is based on the construction of approximated models which combine the Galerkin method at the boundary and regularization processes in the bulk of the domain. The main difficulty is handling the degeneration of the background density profile at the boundary. [ABSTRACT FROM AUTHOR]

The eigenvalue assignment problem of second-order singular system is investigated by using acceleration–velocity–displacement feedback. The conditions are established to ensure the solvability of partial eigenvalue assignment problem of second-order singular system. The derived results are extended to complete eigenvalue assignment problem of second-order singular system. The presented solvability conditions are easily tested. Then, the methods are given to solve the eigenvalue assignment problem of second-order singular systems. Finally, several examples are given to validate our results and algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a novel sliding mode preview control (SMPC) problem with H ∞ performance is investigated for a category of discrete-time singular Markovian jump systems (SMJSs). A novel augmented error system (AES) model is first developed for discrete-time SMJSs based on the analysis of preview information, and the problem of SMPC is reformulated as the stability problem of AES. Secondly, a novel mode-independent sliding surface function is established for AES such that the reachability of sliding mode surfaces (SMS) can always be achievable. Thirdly, sufficient conditions of the H ∞ admissible stability for sliding mode dynamics is derived, based on which a suitable SMPC law is designed to satisfy discrete-time reachability condition. Finally, simulation results have shown that the proposed SMPC law is superior to the control law without previewable information. [ABSTRACT FROM AUTHOR]

In general, the construction of observers for nonlinear descriptor systems depends on the solvability of a linear matrix inequality involving system matrices, and it is based on the system's nonlinearity. Therefore, the type of nonlinearity present in the system heavily affects the observer design process. There are significant developments in the literature for observer design for descriptor systems with various types of nonlinearity. Motivated by this, the current work reviews the literature on observer design for nonlinear descriptor systems with an extensive discussion on the type of nonlinearities that are considered. Here, an analysis and the comparison on the most common nonlinearities is presented, providing a roadmap to all researchers in the field. Furthermore, less common nonlinearities have been identified, presenting under-explored areas within the literature, and can open new domains for future research. [ABSTRACT FROM AUTHOR]

The paper deals with the existence of solutions for quasilinear elliptic systems involving singular and convection terms with variable exponents. The approach combines the sub-supersolutions method and Schauder's fixed point theorem.

This article addresses the issue of iterative learning control for a specific category of discrete linear singular time-delay systems. A new iterative learning control algorithm based on the p-accelerated normal S-iteration method is proposed, and convergence analysis of the corresponding learning control algorithm is studied. With certain assumptions, the proposed algorithm guarantees that the output of the system converges to the desired output trajectory within a finite time interval. The theoretical analysis is supported by numerical examples. The results indicate that the p-accelerated normal S-iterative learning control algorithm outperforms both the first-order PD-type iterative learning control and second-order PD-type iterative learning control algorithms for discrete linear singular systems theoretically and numerically. [ABSTRACT FROM AUTHOR]

The paper deals with the existence of solutions for quasilinear elliptic systems involving singular and convection terms with variable exponents. The approach combines the sub-supersolutions method and Schauder's fixed point theorem. [ABSTRACT FROM AUTHOR]

This paper considers the issues of the admissibility and robust stabilization of fractional‐order singular systems with polytopic uncertainties and fractional‐order α:1≤α<2$$ \alpha :1\le \alpha <2 $$ and 0<α<1$$ 0<\alpha <1 $$. Firstly, the novel admissibility conditions for nominal fractional‐order singular systems are proposed with no conservatism and without any equalities or nonstrict inequalities. Secondly, the robust admissibility conditions for fractional‐order singular systems with polytopic uncertainties are given based on the admissibility conditions for nominal fractional‐order singular systems. Thirdly, to make the uncertain fractional‐order singular systems robustly admissible, the methods of designing the static output feedback controllers are obtained with wider application scope, which are direct, concise, and more relaxed compared with the existing results. All the results are proposed in terms of linear matrix inequalities. Finally, three illustrative examples are given to demonstrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

This paper investigates the admissibility and robust stabilization of fractional-order singular discrete systems with interval uncertainties. Firstly, based on the analysis of the regularity, causality and stability, novel admissibility conditions for nominal fractional-order singular discrete systems are derived including a necessary and sufficient condition in terms of spectral radius and a sufficient condition in terms of non-strict linear matrix inequalities. In order to eliminate the coupling terms and propose strict linear matrix inequality results, another novel admissibility condition is obtained, which is more tractable and reliable with the available linear matrix inequality software solver and more suitable for the controller design compared with the existing results. Secondly, the state feedback controller synthesis for the fractional-order singular discrete systems with interval uncertainties is addressed and the state feedback controller is designed. Finally, the efficiency of the proposed method is demonstrated by two numerical simulation examples. [ABSTRACT FROM AUTHOR]

This paper concerns a nonhomogeneous singular fractional order system, with two frictional damping terms. This system can be considered as a generalization of the so-called Timoshenko system. Results on the existence, uniqueness, and continuous dependence on the solution were obtained via an energy approach, which mainly relies on a priori bounds and density arguments. The approach relies on functional analysis tools and operator theory. Very few results concerning the well-posedness of fractional order Timoshenko systems can be found in the literature. Our results generalize and improve the previous ones and significantly boost the development of the used method. [ABSTRACT FROM AUTHOR]

In this study, for a linear singular system, the dissipativity and disturbance-rejection problems are considered simultaneously. An improved equivalent-input-disturbance (IEID) method has shown good disturbance-rejection performance for linear systems. Therefore, the objective of this study is to obtain a satisfactory disturbance-rejection performance and dissipativity performance level based on the IEID method for singular systems. First, the influence of exogenous disturbances on the system is estimated based on the IEID method. The estimate is added to the control input channel to offset this influence. A necessary and sufficient condition is obtained to ensure that the singular system is admissible and satisfies dissipativity performance level. Subsequently, a state-feedback controller is designed based on the admissibility condition. Finally, a numerical example is used to demonstrate the validity of the proposed method. [ABSTRACT FROM AUTHOR]

This paper discusses an observer-based fuzzy control problem for uncertain nonlinear singular systems under Multi-Performance Requirements (MPRs). The approach used in the paper is to model the system using a Takagi–Sugeno (T-S) fuzzy model that can be analyzed using linear control theories. The proposed control scheme is based on the Parallel Distributed Compensation (PDC) approach and Proportional Derivative (PD) control scheme. The goal is to design an observer-based fuzzy controller that achieves stability of the system and also satisfies the Guarantee Cost Control (GCC) constraint while maintaining a desired passive constraint. The stability analysis is performed using Lyapunov theory, and the sufficient conditions are transformed into a Linear Matrix Inequality (LMI) form using a Shur Complement, free-weighting matrix method and Singular Value Decomposition (SVD) techniques. The LMI conditions are then solved using convex optimization algorithms. Finally, the proposed control method is validated using a bio-economic system to demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]

Noether theorems for two fractional singular systems are discussed. One system involves mixed integer and Caputo fractional derivatives, and the other involves only Caputo fractional derivatives. Firstly, the fractional primary constraints and the fractional constrained Hamilton equations are given. Then, the fractional Noether theorems of the two fractional singular systems are established, including the fractional Noether identities, the fractional Noether quasi-identities and the fractional conserved quantities. Finally, the results obtained are illustrated by two examples. [ABSTRACT FROM AUTHOR]

In this manuscript, we establish the controllability results for a nonlinear singular switched system on arbitrary time scales. We used the mathematical induction to evaluate the solution of the nonlinear slow switched subsystem and nonlinear fast switched subsystem. Also, we study the necessary and sufficient conditions for the controllability of the nonlinear singular switched system followed by the controllability of both the nonlinear switched subsystems. The tools for study include Banach fixed point theorem and pseudo‐inverse of matrices. At last, we illustrate an example to show the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

This essay discusses the H∞$$ {H}_{\infty } $$ control for continuous‐time singular systems with two types of stochastic cyber attacks and dynamic event‐triggered scheme. So as to economize network resources and reduce communication burden, the novel dynamic event‐triggered mechanism is given. Cyber attacks occur randomly during network information transmission, especially the denial of service (DoS) attacks and the deception attacks. By using Lyapunov–Krasovskii functional, some novel sufficient conditions for the impulse free, regular, and asymptotically stable of the studied system are obtained, and a corresponding controller is devised. In addition, a desired controller gain is received through resolving linear matrix inequalities. Eventually, a few numerical examples are supplied to certify the usefulness of provided design ways and results. [ABSTRACT FROM AUTHOR]

We investigate exponential admissibility of singular systems with multiply variable delays. We give new criteria such that the systems are regular, impulse-free (IF) and exponentially stable (ES). The techniques of the proofs are based on the Lyapunov- Krasovskiĭ functional (LKF), convex polyhedron methods and linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the obtained results. Using MATLAB-Simulink software, the trajectories of the solutions are provided. This study generalizes and improves certain results in the present literature. [ABSTRACT FROM AUTHOR]

In this paper we deal with the following singular-regular anisotropic system - L u = - ∑ i = 1 N ∂ i ∂ i u p i - 2 ∂ i u = p v q u 1 - p i n Ω , - L v = - ∑ i = 1 N ∂ i ∂ i v p i - 2 ∂ i v = q v q - 1 u p i n Ω , u > 0 and v > 0 i n Ω , u = 0 and v = 0 o n ∂ Ω , where Ω is a bounded regular domain in R N and 1 ≤ p 1 ≤ p 2 ≤ ⋯ ≤ p N. Under some suitable conditions on the parameters p and q, we obtain existence results by using nondifferentiable variational techniques. [ABSTRACT FROM AUTHOR]

In this paper, the problem of dissipativity filtering for discrete-time nonlinear singular systems with distributed delays is addressed. An interval type-2 fuzzy model is employed to represent the nonlinear singular systems of which the parameter uncertainties are captured by interval type-2 membership functions characterized by lower and upper membership functions. Based on event-triggering scheme, an interval type-2 filter is proposed. By adopting the idea of input delay method, the filtering error systems is reformulated as a new event-triggering interval type-2 fuzzy singular systems with mixed time-delays. By using an improved reciprocally convex combination approach and some new techniques on matrix convexification to bound the forward difference of the double and the triple summation terms in the Lyapunov function, two less conservatism conditions have been derived. The event-triggered dissipative filter gains and the event-triggering parameters are obtained to determine the filter error singular systems admissible and dissipative. A numerical example is given to illustrate the effectiveness of this proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the stabilization problem for a class of discrete-time semi-Markov jump singular systems with mode-dependent singular matrix. Since our model is mode-dependent singular matrix, the previous methods are unable to achieve the stability. To overcome this difficulty, the novel and less conservative stability conditions with the original system coefficient matrices are constructed by developing new theories and methods. Based on the above conditions, the linear matrix inequality (LMI) based stabilizing controller design method is proposed. [ABSTRACT FROM AUTHOR]

This paper further investigates the problem of reachable set estimation (RSE) for a class of continuous-time singular systems with time-varying delay. First, we use the relaxed Lyapunov–Krasovskii functional to tackle the RSE problem. This functional does not need all the matrices concerned to be positive definite. In addition, a novel weighted integral inequality and time-delay partition approach are utilized to reduce conservatism in the results. Based on these methods, sufficient conditions in the form of linear matrix inequalities are established. Finally, the correctness and validity of these relaxed results are demonstrated by three simulation examples. [ABSTRACT FROM AUTHOR]

The Hamiltonian analysis for the linearized λ R gravity plus a Chern–Simons term is performed. The first-class and second-class constraints for arbitrary values of λ are presented, and one physical degree of freedom is reported. The second-class constraints are removed, and the corresponding generalized Dirac brackets are constructed; then, the difference between theories with different values of λ is remarked. [ABSTRACT FROM AUTHOR]

This paper addresses the H ∞ filtering for discrete-time Markovian jump singular systems (MJSSs). While the existing researches have only given the sufficient conditions, in this paper a sufficient and necessary condition is established to guarantee that the filtering error system is regular, causal, stochastically stable and H ∞ performance in light of supermartingale-liked approach and property of conditional expectation as well as – bounded real lemma. For obtaining the filter, an equivalent matrix inequality to the obtained one in nonlinear form is provided in terms of congruence transformation. Thus the desired filter can be developed by choosing matrix variables with certain structures. Finally, two simulations are provided to show the effectiveness of the proposed techniques in this paper. [ABSTRACT FROM AUTHOR]

Applied in many fields, nonlinear systems involving delay and algebraic equations are referred to as singular systems. These systems remain challenging due to saturation constraints that affect actuators and cause harm to their operation. Furthermore, the complexity of the problem will increase when uncertainty also simultaneously affects the system under consideration. To address this issue, this paper investigated a feasible control strategy for nonlinear singular systems with time-varying delay that are subject to uncertainty and actuator saturation. The IT-2 fuzzy model was adopted to describe the dynamic of the non-linear delayed systems using lower and upper membership functions to deal with the uncertainty. Moreover, the polyhedron model was applied to characterize the saturation function. The goal of the control approach was to design a relevant IT2 fuzzy state feedback controller with mismatched membership functions so that the closed-loop system is admissible. On the basis of an appropriate Lyapunov–Krasovskii functional, sufficient delay-dependent conditions were established and an optimization problem was formulated in terms of linear matrix inequality constraints to optimize the attraction domain. Simulation examples are provided to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

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Noether’s symmetry and conserved quantity of singular systems under generalized operators were studied. Firstly, the Lagrangian equation of singular systems under generalized operators was established, and the primary constraints on the system were derived. Then the Lagrangian multiplier was introduced to establish the constrained Hamilton equation and the compatibility condition under generalized operators. Secondly, based on the invariance of the Hamilton action under the infinitesimal transformation, Noether’s theorem for constrained Hamiltonian systems under generalized operators was established, and the symmetry and corresponding conserved quantity of the system were given. Under certain conditions, Noether’s conservation of constrained Hamiltonian systems under generalized operators can be reduced to Noether’s conservation of integer-order constrained Hamiltonian systems. Finally, an example illustrates the application of the results. [ABSTRACT FROM AUTHOR]

There are countless applications of non-linear systems that incorporate delay and algebraic equations. Despite current improvements in control theory, stochastic actuator defects still pose challenges when it comes to these systems. Furthermore, when it is not possible to measure the states of the system, and when uncertainties affect the system under investigation, the problem becomes even more complex. This paper is concerned with fault-tolerant observer-based controller synthesis for non-linear delayed singular systems with uncertainties and stochastic actuator failures. On the basis of interval valued models, a new Lyapunov-Krasovskii functional is built to develop a less conservative criterion to ensure that the closed-loop system is admissible in the mean-square sense. In addition, as these matrices are coupled with multiple variables, finding the parametric matrices of the observer and controller in terms of the obtained condition is more complex and challenging. The proposed method employs the matrix inequality decoupling technique to resolve this issue. Eventually, simulations are carried out to demonstrate the applicability of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper we study vector-valued almost minimizers of the energy functional ∫ D (| ∇ u | 2 + 2 | u |) d x. We establish the regularity for both minimizers and the "regular" part of the free boundary. The analysis of the free boundary is based on Weiss-type monotonicity formula and the epiperimetric inequality for the energy minimizers. [ABSTRACT FROM AUTHOR]

In this brief, the finite-time peak-to-peak filter design problem is investigated for discrete-time nonlinear singular system. The T-S fuzzy model is introduced to represent the considered nonlinear system. First, a useful analysis method is proposed to detect whether the resulting filtering error system is singular finite-time bounded and guarantees the peak-to-peak performance. Further, in order to cope with the difficulty caused by the special form of filtering error system, we propose a novel filter form which facilitates the elimination of the coupling items in the filter design. And based on this, the sufficient design scheme for finite-time peak-to-peak filter is formulated by means of standard linear matrix inequality technique. Finally, a tunnel diode circuit is used to illustrate the feasibility and effectiveness of the developed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the finite-time stability problem of singular Markovian jump systems with time-varying delay. Firstly, this paper presents some new inequalities which are very important to the finite-time stability problem of the considered systems. Secondly, by employing these new inequalities and the Lyapunov–Krasovskii functional approach, this paper derives some sufficient conditions that guarantee the considered systems to be regular, impulse-free and finite-time stable. Finally, three numerical examples are given to illustrate the effectiveness and advantage of the proposed methods. • The finite-time stability problem for the singular Markovian systems with time-varying delay is studied in this paper. • Some new inequalities are presented in this paper. • By employing the obtained new inequalities, some new sufficient conditions which guarantee the considered systems to be regular, impulse-free and finite-time stable are derived. • Three numerical examples are given to illustrate the effectiveness and advantage of the proposed methods. [ABSTRACT FROM AUTHOR]

The current investigations present the numerical solutions of the novel singular nonlinear fifth-order (SNFO) system of multi-pantograph differential model (SMPDM), i.e., SNFO–SMPDM. The novel SNFO–SMPDM is obtained using the sense of the second kind of typical Emden–Fowler and prediction differential models. The features of shape factor, pantograph along with singular points are provided for all four obtained classes of the SNFO–SMPDM. The extensive use of the singular models is observed in the engineering and mathematical systems, e.g., inverse systems and viscoelasticity or creep systems. For the correctness of the proposed novel SNFO–SMPDM, one case of each class is numerically handled by applying supervised neural networks (SNNs) along with the optimization of Levenberg–Marquardt backpropagation scheme (LMBS), i.e., SNNs–LMBS. A dataset using the traditional variational iteration scheme is designed to compare the proposed results of each case of SNFO–SMPDM. The obtained approximate solutions of each class using the novel SNFO-SMPDM are presented based on the training (80 %), authentication (10 %) and testing (10 %) measures to evaluate the mean square error. Fifteen numbers of neurons, and sigmoid activation function are used in this SNN process. To authenticate the competence, and precision of SNFO–SMPDM, the numerical simulations are accessible by applying the relative measures of regression, error histogram plots, and correlation. [ABSTRACT FROM AUTHOR]

This paper considers the problems of stochastic admissibility and extended dissipativity analysis, as well as dynamical output feedback controller design for interval type-2 singular semi-Markovian jump fuzzy systems. By utilising the partition method and the matrix decomposition technique, an improved approach of handling the time-varying transition rates is proposed. Based on this approach, a sufficient condition with less conservatism is established to guarantee that the closed-loop system is regular, impulse-free, exponentially stable in mean square and extended dissipative. Determining the parametric matrices of the controller via the obtained sufficient condition is difficult, since some parametric matrices factor between two nonsquare matrices. A dynamical output feedback control scheme is proposed by utilising a vital result which is proposed inspired by Projection lemma. It is worth noting that no conservatism is introduced in controller design due to the sufficiency and necessity of this result. Finally, simulation examples are given to show the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Singular systems play an important role in many fields, and some new fractional operators, which are general, have been proposed recently. Therefore, singular systems on the basis of the mixed derivatives including the integer order derivative and the generalized fractional operators are studied. Firstly, Lagrange equations within mixed derivatives are established, and the primary constraints are presented for the singular systems. Then the constrained Hamilton equations are constructed by introducing the Lagrange multipliers. Thirdly, Noether symmetry, Lie symmetry and the corresponding conserved quantities for the constrained Hamiltonian systems are investigated. And finally, an example is given to illustrate the methods and results. [ABSTRACT FROM AUTHOR]

In this article, admissibility problem for a kind of singular systems with delays is studied. Firstly, the given singular system with delays is transformed into a neutral system with delays. Secondly, new sufficient criteria are obtained on the stability of the new neutral system by aid of Wirtinger-based integral inequality, linear matrix inequality (LMI) and suitable Lyapunov-Krasovskii functionals (LKFs). The obtained criteria are valid for both of the systems. At the end, two numerical examples are given to illustrate the applicability of the obtained results using MATLAB-Simulink software. By this article, we extend and improve some results of the past literature. [ABSTRACT FROM AUTHOR]

This article, based on dissipativity theory, aims to tackle the consensus tracking issue for Lipschitz nonlinear singular multiagent systems (MASs) with switching topologies and communication delays. Rooted at the leader node, a directed spanning tree is assumed to be contained in the union of all possible interaction graphs. Within the framework of topology switching controlled by a Markov chain, communication delays encountered in the data transmission process are reasonably considered to be time-varying and dependent on Markovian jump modes. By using tools from the stochastic Lyapunov functional technique, algebraic graph theory, and strict $(\mathcal {Q},\mathcal {S},\mathcal {R})-\bar {\alpha }$ -dissipativity analysis, the consensus controller collecting delayed in-neighboring agents’ information is designed to ensure stochastic admissibility and strict dissipativity of the resulting consensus error system. The theoretical analysis is validated by numerical simulations. [ABSTRACT FROM AUTHOR]

Uncertainty theory is a new branch of mathematics concerned with the analysis of subjective indeterminacy. Based on the concept of uncertain theory, this paper considers optimal control and zero-sum differential game for multi-factor uncertain continuous-time singular systems with Hurwicz criterion, where dynamic systems are modelled by a type of uncertain differential equation driven by canonical Liu process. Using the approach of dynamic programming, the principle of optimality is proposed and then the equation of optimality is derived to resolve an uncertain control model. A two-player zero-sum uncertain differential game is further investigated based on the optimality equation above, and an equilibrium equation is presented to locate a saddle-point in the game. Finally, an example is discussed to illuminate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

In this paper we show existence and multiplicity of positive solutions using the sub-supersolution method and Mountain Pass Theorem in a general singular system which the operator is not homogeneous neither linear.

This work focuses on the stabilization issue for a class of singular stochastic systems against fractional Gaussian noise driven by fractional Brownian motion. In particular, the system is formulated with time-delay, nonlinear actuator faults and randomly occurring parameter uncertainties. Primarily, a fractional-infinitesimal operator is incorporated to deal with the fractional Ito stochastic systems in the derivation part of Lyapunov-based stability analysis. Further, the considered system is subjected to both linear and nonlinear actuator faults and the stabilization will be achieved by the consideration of a nonlinear resilient fault-tolerant proportional-retarded controller. By incorporating the fractional-infinitesimal operator and with the choice of a relevant Lyapunov-Krasovskii functional candidate, a new adequate criterion is deduced by means of linear matrix inequalities. Then the established inequalities are then solved for obtaining the controller gain matrices. Thereafter, an example illustrating the effectiveness and applicability of the proposed results is provided.

This paper addresses the robust finite-time $H_\infty $ control problem for the uncertain singular system by using the stability theory of dynamical systems. Firstly, a lemma is provided to show that the singular system is finite-time stability by using the state space decomposition approach. Similar with the proof method of this Lemma, the singular system is divided into a differential system and an algebra one. Then, some conditions are derived to ensure the singular system being finite-time $H_\infty $ stability based on the obtained lemma, and the state feedback control law is designed. These conditions are provided in the form of the linear matrix inequalities and can be easily solved. Finally, a numerical example is given to illustrate the effectiveness of the obtained results.

In this paper, we point out the main disadvantage of the existing methods for solving an inverse source problems: The smoothness of the solutions is limited by the boundary condition. A Fourier extension method with a modified Tikhonov regularization is presented to overcome the limitation. Compared with previous studies, the convergence result of the new method is established under a weaker a priori assumption. Numerical experiments further verify the advantage of the method. [ABSTRACT FROM AUTHOR]

In this paper, the finite time stability and H∞ finite-time stability of singular linear systems are considered. By constructing a class of time-dependent Lyapunov functions and introducing a zero term with free weighting matrices, we first establish a new explicit criterion in the form of LMIs for finite-time stability of the system. Then, an H∞ finite-time stability criterion for the system is obtained. The given results are easily verifiable and less conservative compared with some existing ones in the literature. Finally, four numerical examples are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Requirements are investigated in this paper for each descriptor form subsystem, with which a causal/impulse free networked dynamic system (NDS) can be constructed. For this purpose, a matrix rank-based necessary and sufficient condition is at first derived for the causality/impulse freeness of an NDS, with the matrix depending affinely on subsystem connections. From this result, a necessary and sufficient condition is derived on each subsystem for causal/impulse free NDS constructibility. This condition further leads to a necessary and sufficient condition for the existence of a local static output feedback that guarantees the construction of a causal/impulse free NDS. Remarkably, all the numerical computations involved in these conditions are performed independently on each individual subsystem. Situations have also been clarified in which NDS causality/impulse freeness is independent of subsystem connections. It has also been made clear that local static output feedbacks may not be helpful in constructing a causal NDS. [ABSTRACT FROM AUTHOR]

This paper investigated the almost surely exponential stability (ES a.s.) for semi‐Markovian switched singular stochastic systems (SSSSs) with mode‐dependent ranks, in which the derivative matrices Ei have different ranks. Due to the constraint of consistent initial conditions, state jumps may occur at switching instants in switched singular systems. Some more general conditions for the existence and uniqueness of the solution of semi‐Markovian SSSSs with mode‐dependent ranks are given together with a detailed analysis of state jumps. Based on the equivalent systems transformation and multiple Lyapunov functions method, novel conditions of ES a.s. are presented for addressed systems. An example is given to explain the effectiveness of developed results. [ABSTRACT FROM AUTHOR]