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We establish sufficient conditions for the exponential stability of nonsingular impulsive delayed integro‐differential systems. Our approach to addressing nonsingular differential problems involves the application of permutable matrices and their associated delayed exponential. Furthermore, we investigate the controllability of a nonlinear impulsive and delayed problem by employing the corresponding Gramian matrix. Finally, to illustrate the theoretical outcomes, we provide examples and graphical representations for each situation. [ABSTRACT FROM AUTHOR]

In this research paper, we investigate the controllability in the α -norm of a coupled system of integrodifferential equations with state-dependent nonlocal conditions in generalized Banach spaces. We establish sufficient conditions for the system's controllability using resolvent operator theory introduced by Grimmer, fractional power operators, and fixed-point theorems associated with generalized measures of noncompactness for condensing operators in vector Banach spaces. Finally, we present an application example to validate the proposed methodology in this research. [ABSTRACT FROM AUTHOR]

The purpose of this work is to investigate the controllability of non-instantaneous impulsive (NII) Hilfer fractional (HF) neutral stochastic evolution equations with a non-dense domain. We construct a new set of adequate assumptions for the existence of mild solutions using fractional calculus, semigroup theory, stochastic analysis, and the fixed point theorem. Then, the discussion is driven by some suitable assumptions, including the Hille–Yosida condition without the compactness of the semigroup of the linear part. Finally, we provide examples to illustrate our main result. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we present a lemma that allows us to characterize a broad class of C0-semigroups on time scales, which can be applied to prove existence and uniqueness of solutions of systems of partial differential equations where the time domain is a time scale. The result obtained is applied to study the controllability of the heat equation on time scales. The lemma presented in this paper can be seen as a unification of the one proved by H. Leiva in [28], for semigroups in [0,∞). [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of developing a unified method for quantifying and improving the cyber resilience of large-scale cyber-physical systems (CPSs) against cyber-attacks targeting structural controllability. To this end, we provide necessary and sufficient conditions to extend the concept of structural controllability of single-layer systems to two-layer CPSs comprising of power network as the physical layer and communication network as the cyber layer. Next, in order to assess cyber resilience, we introduce the notion of $ R $ R -resilient CPS as the maximum number of cyber nodes that can be attacked by an adversary while preserving the structural controllability of the entire CPS. Furthermore, we provide an algorithm to find the optimal network reconfiguration matrix to increase the resilience level of CPS from $ R $ R -resilient to $ ({R + 1}) $ (R + 1) -resilient by adding a minimum number of transmission lines to the physical layer or communication links to the cyber layer, or both. Additionally, the proposed methodology is extended to achieve $ ({R + \alpha }) $ (R + α) -resilient CPS, where α>1. The effectiveness of the proposed method is verified through simulations of IEEE 14, IEEE 39, and IEEE 118 power networks with different cyber topologies, considering four scenarios of denial-of-service (DoS) attacks, including targeted and random node attacks. [ABSTRACT FROM AUTHOR]

In this paper, we consider a system of two degenerate wave equations coupled through the velocities, only one of them being controlled. We assume that the coupling parameter is sufficiently small and we focus on null controllability problem. To this aim, using multiplier techniques and careful energy estimates, we first establish an indirect observability estimate for the corresponding adjoint system. Then, by applying the Hilbert Uniqueness Method, we show that the indirect boundary controllability of the original system holds for a sufficiently large time. [ABSTRACT FROM AUTHOR]

This work investigates the solvability of the generalized Hilfer fractional inclusion associated with the solution set of a controlled system of minty type–fuzzy mixed quasi-hemivariational inequality (FMQHI). We explore the assumed inclusion via the infinite delay and the semi-group arguments in the area of solid continuity that sculpts the compactness area. The conformable Hilfer fractional time derivative, the theory of fuzzy sets, and the infinite delay arguments support the solution set's controllability. We explain the existence due to the convergence properties of Mittage–Leffler functions ( E α , β ), that is, hatching the existing arguments according to FMQHI and the continuity of infinite delay, which has not been presented before. To prove the main results, we apply the Leray–Schauder nonlinear alternative thereom in the interpolation of Banach spaces. This problem seems to draw new extents on the controllability field of stochastic dynamic models. [ABSTRACT FROM AUTHOR]

This paper is devoted to the local null-controllability of the nonlinear KdV equation equipped the Dirichlet boundary conditions using the Neumann boundary control on the right. Rosier proved that this KdV system is small-time locally controllable for all noncritical lengths and that the uncontrollable space of the linearized system is of finite dimension when the length is critical. Concerning critical lengths, Coron and Crépeau showed that the same result holds when the uncontrollable space of the linearized system is of dimension 1; later Cerpa, and then Cerpa and Crépeau, established that the local controllability holds at a finite time for all other critical lengths. In this paper, we prove that, for a class of critical lengths, the nonlinear KdV system is not small-time locally controllable. [ABSTRACT FROM AUTHOR]

In biological systems, impulses are often used to model mutations in gene expression. In order to describe the instantaneity of the impulse, this paper employs a hybrid‐index model of impulsive Boolean networks with state‐triggered impulses. Based on this model, the time‐domain output controllability is investigated. Using the quotient mapping method, the hybrid‐domain solutions of this model are mapped to the time‐domain solutions, mathematically. Then a necessary and sufficient condition for output controllability in the time domain is presented. Finally, an example is given to demonstrate the correctness and effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This work studies the controllability of a class of Riemann–Liouville fractional differential equations of order 1<ς<2$$ 1<\varsigma <2 $$ in a new Banach space Zς−1$$ {Z}_{\varsigma -1} $$ using fractional cosine family. To derive the existence of solutions, we construct the definition of mild solutions of the system using Laplace transform theory. Then, by assuming the approximate controllability of corresponding linear equation, we prove that the nonlinear dynamical system is approximately controllable using an iterative technique. Lastly, we give an example to illustrate the established theory. [ABSTRACT FROM AUTHOR]

The purpose of this work is to investigate the exponential stability of a second‐order coupled wave equations by Laplacian with one locally internal viscous damping. The strong stability is established by combining a unique continuation result and a Carleman estimate. Besides, the exponential stability is proved under (PMGC) condition on the damping region without any restriction on wave propagation speed (i.e., whether the two wave equations propagate at the same speed or not). The proof of this result relies on the frequency domain method combined with the multiplier techniques. [ABSTRACT FROM AUTHOR]

Sotol bagasse (SB) is a byproduct generated during the fermentation of the sotol plant (Dasylirium sp.) for the production of a traditional alcoholic beverage in Mexico. In this study, a novel ethanol purification distillation sequence is proposed, utilizing ethanol produced from SB treatment as described by González-Chavez et al. (2022). Prior to purification, the ethanol-water mixtures exhibited ratios of 0.054 and 0.935. The proposed distillation sequence comprises three columns: i) depletion, ii) extraction (employing ethylene glycol as the solvent agent), and iii) solvent recovery. To assess energy consumption and controllability, three solvent:feed ratios (1.5:1, 2:1, 2.5:1) were examined, taking into account the feed to the second column. The lowest energy consumption was observed at 31 × 103 kW, corresponding to the 1.5:1 ratio. Optimal controllability was achieved at a solvent:feed ratio of 2.5:1, as evidenced by the lowest Integral Absolute Error (IAE) value of 3.3 × 10–3 and the highest proportional gain (Kc) value of 250. In summary, we leveraged previously reported experimental data to design a new distillation sequence with potential applications in the ethanol purification derived from SB fermentation. The outcomes of this investigation underscore the importance of promoting circular economy practices, particularly in the northern region of Mexico, where significant quantities of agrowastes are generated. [Display omitted] • The dynamic control properties of an ethanol-water azeotropic mixture obtained from BS were determined. • The controllability increases with the increase in solvent. • The energy expenditure decreases as the solvent decreases. [ABSTRACT FROM AUTHOR]

We consider an optimal control problem on the fixed interval of time with the right endpoint constraint. We introduce the concept of controllability for this problem. The main result of the paper states that if for the optimal control problem the Pontryagin maximum principle fails on the given admissible process then this process satisfies the controllability condition. [ABSTRACT FROM AUTHOR]

We consider a smooth system of the form q ˙ = f 0 (q) + ∑ i = 1 k u i f i (q) , q ∈ M , u i ∈ R , and study controllability issues on the group Diff M . It is well-known that the system can arbitrarily well approximate the movement in the direction of any Lie bracket polynomial of f 1 , … , f k . Any Lie bracket polynomial of f 1 , … , f k is good in this sense. Moreover, some combinations of Lie brackets which involve the drift term f 0 are also good but surely not all of them. In this paper, we try to characterize good ones and, in particular, all universal good combinations, which are good for any nilpotent truncation of any system. [ABSTRACT FROM AUTHOR]

We consider the local null controllability of a modified Navier–Stokes system where we include nonlocal spatial terms. We generalize a previous work where the nonlocal spatial term is given by the linearization of a Ladyzhenskaya model for a viscous incompressible fluid. Here, the nonlocal spatial term is more general and we consider a control with one vanishing component. The proof of the result is based on a Carleman estimate where the main difficulty consists in handling the nonlocal spatial terms. One key point corresponds to a particular decomposition of the solution of the adjoint system that allows us to overcome regularity issues. With a similar approach, we also show the existence of insensitizing controls for the same system. [ABSTRACT FROM AUTHOR]

An algorithm for finding a control of a linear switched system by means of Geometric Algebra is designed. More precisely, we develop a switching path searching algorithm for a two‐dimensional linear dynamical switched system with a non‐singular matrix whose integral curves are formed by two sets of centralized ellipses. It is natural to represent them as elements of Geometric Algebra for Conics and construct the switching path by calculating switching points, i.e., intersections and contact points. For this, we use symbolic algebra operations or, more precisely, the wedge and inner products that are realizable by sums of products in the coordinate form. Therefore, no numerical solver to the system of equations is needed. Indeed, the only operation that may bring in an inaccuracy is vector normalization, i.e., square root calculation. The resulting switching path is formed by pieces of ellipses that are chosen, respectively, from the two sets of integral curves. The switching points are either intersections in the first or final step of our algorithm, or contact points. This choice guarantees the optimality of the switching path with respect to the number of switches. Two examples are provided to demonstrate the search for the intersections of the conics and, consequently, a description is presented of the construction of a switching path in both cases. [ABSTRACT FROM AUTHOR]

In this study, our main focus is on the analysis of the existence, controllability, and Hyers–Ulam stability of a neutral switched system with impulsive effects on non-uniform time domains. First, we use the Banach fixed point theorem and the time scales calculus to explore the existence, Ulam's type stability, and controllability of a considered switched system. In the end, we examine the controllability results through numerical simulations. This article aims to identify the essential requirements for achieving controllability and stability on different time scales. [ABSTRACT FROM AUTHOR]

The quotient space method provides a novel idea for modelling the transient dynamics of dimension-varying control systems. This paper investigates the realisation problem of the transient dynamics of dimension-varying control systems. By revealing the structure of the controllable subspace for the linear system on quotient space, we propose the condition for the realisation of the transient dynamics of dimension-varying control systems, based on which a new scheme for modelling the transient dynamics is given. Moreover, the proposed scheme justifies the existing result for the strategy for modelling the transient dynamics. A numeric example is given to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

AbstractAccording to SAMHSA (2023), approximately 16,600,000 American adults and teens reported having serious thoughts of suicide in 2022. While suicide prevention has primarily focused on suicide deaths and attempts, we contend that suicidal ideation (SI) deserves more in-depth investigation and should be an essential intervention target on its own. In support of this point, we provide three examples of ways to improve specificity in understanding of SI through the study of controllability of SI, the language used to assess SI, and measuring SI in real time. We also consider qualitative work on the content of SI, its treatment, and definitional considerations. We thus call for an increased general focus on SI within research, clinical care, and policy. [ABSTRACT FROM AUTHOR]

The moment method is used to prove the exact controllability of a wide class of bidimensional linear dispersive PDE's posed on the two-dimensional torus T². The control function is considered to be acting on a small vertical and horizontal strip of the torus. Our results apply to several well-known models including some bidimesional extensions of the Benajamin--Ono and Korteweg--de Vries equations. As a by product, the exponential stabilizability with any given decay rate is also established in the Sobolev space Hsp(T²), with s ≥ 0, by constructing an appropriated feedback control law. [ABSTRACT FROM AUTHOR]

Controllability is a fundamental issue in the field of fractional complex network control, yet it has not received adequate attention in the past. This paper is dedicated to exploring the controllability of complex networks involving the Caputo fractional derivative. By utilizing the Cayley–Hamilton theorem and Laplace transformation, a concise proof is given to determine the controllability of linear fractional complex networks. Subsequently, leveraging the Schauder Fixed-Point theorem, controllability Gramian matrix, and fractional calculus theory, we derive controllability conditions for nonlinear fractional complex networks with a weighted adjacency matrix and Laplacian matrix, respectively. Finally, a numerical method for the controllability of fractional complex networks is obtained using Matlab (2021a)/Simulink (2021a). Three examples are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper introduces a methodology for examining finite-approximate controllability in Hilbert spaces for linear/semilinear ν -Caputo fractional evolution equations. A novel criterion for achieving finite-approximate controllability in linear ν -Caputo fractional evolution equations is established, utilizing resolvent-like operators. Additionally, we identify a control strategy that not only satisfies the approximative controllability property but also ensures exact finite-dimensional controllability. Leveraging the approximative controllability of the corresponding linear ν -Caputo fractional evolution system, we establish sufficient conditions for achieving finite-approximative controllability in the semilinear ν -Caputo fractional evolution equation. These findings extend and build upon recent advancements in this field. The paper also explores applications to ν -Caputo fractional heat equations. [ABSTRACT FROM AUTHOR]

This work studies the existence of solutions and approximate controllability of fractional integrodifferential systems with Riemann-Liouville derivatives and with multiple delays in control. We establish suitable assumptions to prove the existence of solutions. Controllability of the system is shown by assuming a range condition on control operators and Lipschitz condition on non-linear functions. We use the concepts of strongly continuous semigroup rather than resolvent operators. Finally, an example is give to illustrate the theory. [ABSTRACT FROM AUTHOR]

In our article, we are primarily concentrating on existence and controllability of nonlocal mixed Volterra‐Fredholm type fractional delay integro‐differential equations of order 1 < r < 2. By applying the results and facts belongs to the cosine function of operators, fractional calculus, the measure of noncompactness and fixed point approach, the main results are established. Initially, we focus the existence of mild solution, and later we establish the controllability of the considered fractional system. Finally, we present an example to demonstrate the theory. [ABSTRACT FROM AUTHOR]

In our paper, we primarily concentrate on the existence and controllability results for fractional evolution inclusions of order 1 < r < 2 with Clarke's subdifferential type. By applying the facts related to the measure of noncompactness, fractional calculus, and fixed‐point technique, the principal results are proved. Initially, we are concentrating the existence and continue to prove the controllability of the fractional evolution system. In the end, we present an example to demonstrate the theory. [ABSTRACT FROM AUTHOR]

In this paper, we prove the boundary exact local controllability around ground state solitary waves with different scaling for the mass critical and mass slightly subcritical nonlinear Schrödinger equation. More precisely, we prove that there exists a control driving the solution from the vicinity of Q λ 1 to the vicinity of Q λ 2 , for λ 1 , λ 2 > 0 , with a minimal time of controllability. In the mass slightly subcritical case, we also prove the null controllability for initial data starting in a neighborhood of the ground state Q λ , for λ > 0 , with a minimal time of controllability. The control strategy deployed in this article is non-destructive as the solution remains close to the ground state for all time. [ABSTRACT FROM AUTHOR]

We prove that the solutions of the Schrödinger and biharmonic Schrödinger equations do not have the exact boundary controllability property on the half-line by showing that the associated adjoint models lack observability. We consider the framework of |$L^2$| boundary controls with data spaces |$H^{-1}(\mathbb{R}_+)$| and |$H^{-2}(\mathbb{R}_+)$| for the classical and biharmonic Schrödinger equations, respectively. The lack of controllability on the half-line contrasts with the corresponding dynamics on a finite interval for a similar regularity setting. Our proof is based on an argument that uses the sharp fractional time trace estimates for solutions of the adjoint models. We also make several remarks on the connection of controllability and temporal regularity of spatial traces. [ABSTRACT FROM AUTHOR]

In this work, the consensus problem of multi‐agent systems is addressed whose agent dynamics are described by the switched linear system, and the interaction topology is a directed graph. Two cases are considered: For completely controllable agent dynamics, a novel construct method of control law and switching signal are proposed to derive sufficient conditions to solve the finite‐time consensus problem. When the controllability of the agent system is incomplete, it is proven that the uncontrollable sub‐mode of agent dynamics is consistently asymptotically stabilizable is a key condition to achieve consistency for multi‐agent systems. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical results obtained in this paper. [ABSTRACT FROM AUTHOR]

The eigenstructure of imaginary axis eigenvalues of a Hamiltonian matrix is of importance in many fields of control systems, for example, in stability analysis of linear Hamiltonian systems, computation of the solutions of an algebraic Riccati equation (ARE), existence of a Lyapunov function for LTI systems, etc. The dynamical system consisting of all stationary trajectories for an optimal control problem – often called the Hamiltonian system – is known to admit, in its state space dynamical equation, a Hamiltonian matrix for the system matrix. In each of these cases, defectiveness of imaginary axis eigenvalues of a Hamiltonian matrix turns out to be of crucial importance. For example, defectiveness causes unboundedness of the oscillatory stationary trajectories in the Hamiltonian system. A characterisation of the ARE solutions in terms of Lagrangian invariant subspaces of the Hamiltonian matrix when the imaginary axis eigenvalues are defective has been addressed in the literature for the controllable case. This paper focuses on the general case of uncontrollable systems; we formulate conditions under which the imaginary axis eigenvalues of the Hamiltonian matrix are non-defective: this is central for solutions corresponding to imaginary axis eigenvalues to not become unbounded. We provide conditions on the so-called ϵ -characteristic of the non-defective imaginary axis eigenvalue: this helps in the characterisation of Lagrangian invariant subspaces. We formulate conditions under which a passivity-based Hamiltonian matrix is normal (i.e. it commutes with its transpose), and we link normality of such Hamiltonian matrices with all-pass behaviour. In summary, this paper formulates results that link defectiveness of imaginary axis eigenvalues of Hamiltonian matrix to solvabilities of Lyapunov and Algebraic Riccati equations, controllability/observability, ϵ -characteristic and sign-controllability. We consider examples in the area of bounded-real transfer functions and RLC circuits, both controllable and uncontrollable, to study applicability of the results of this paper. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the controllability of the point vortex system by means of a single vortex. The point vortex system is a well-known simplified model for the incompressible Euler equation, where the vorticity is concentrated in a finite number of Dirac masses. We use one of the vortices as a control and prove that by suitably choosing its trajectory, we can drive all other vortices to a given prescribed position in arbitrary time. [ABSTRACT FROM AUTHOR]

Background: Previous research has shown that the more people believe their emotions are controllable and useful (BECU), the less they generally report psychological distress. Psychological distress, in turn, impacts health outcomes, and is among the most frequently reported complaints in psychotherapeutic and psychosomatic practice. Objective: We aimed to examine how BECU predicts psychological distress related to somatic symptoms in a prospective sample from the general population and to replicate this association in two cross‐sectional samples of psychosomatic patients. Methods: We applied a panel design with an interval of 2 weeks between T1 and T2 in general‐population panel‐participants (N = 310), assessing BECU and psychological distress related to somatic symptoms via validated self‐report measures. Moreover, we cross‐sectionally replicated the relationship between BECU and psychological distress in a clinical sample of psychosomatic outpatients diagnosed with somatoform disorders (n = 101) or without somatoform disorders (n = 628). Results: BECU predicted over and above the lagged criterion panel‐participants' psychological distress related to somatic symptoms, β = −.18, p <.001. BECU was also cross‐sectionally related to psychological distress in our clinical replication‐sample of psychosomatic outpatients diagnosed with somatoform disorders, rS(87) = −.33, p =.002 and in those without, rS(557) = ‐.21, p <.001. Conclusions: BECU as a malleable way of thinking about emotions predicted psychological distress related to somatic symptoms in general‐population panel‐participants and correlated with the same in two clinical replication samples. BECU thus becomes a promising treatment target in psychotherapeutic approaches. [ABSTRACT FROM AUTHOR]

In two studies, we investigated for the first time the content of children's counterfactual thoughts about their own experiences. Results showed that the majority of children aged 8-13 were able to produce valid counterfactuals regarding an event that happened to them, despite not achieving an adult-level ability. Comparing counterfactual and prefactual thinking, in Study 1 we found that children showed the same temporal asymmetry previously found in adults: They focused on the controllable features of their experience more in prefactual than counterfactual thinking. However, in Study 2, comparing counterfactuals produced by children and adults after a task in which making errors became salient, children produced more controllable counterfactuals (modifying their own errors) than adults, who still focused on uncontrollable features (as in Study 1). These results suggest that the ability to reason counterfactually in complex and real-life situations is not yet fully developed at age 8-13 years, affecting counterfactual content. [ABSTRACT FROM AUTHOR]

In this paper, we study the stabilization and the partial exact controllability of an inhomogeneous multidimensional thermoelastic diffusion problem by a memory function introduced on a part of the boundary of the material. By using the Nakao difference inequality, we prove that the energy of the system decays to zero exponentially at a rate determined explicitly by the physical parameters. Then by the Hilbert uniqueness method combined with Russell's principle "controllability via stabilizability," we prove that after certain threshold time moment, the considered system is partially controllable under a smallness restriction on the coupling parameters stress-temperature and stress-diffusion. The boundary control function is determined explicitly. [ABSTRACT FROM AUTHOR]

This paper investigates the possibility of automatically linearizing nonlinear models. Constructing a linearised model for a nonlinear system is quite labor-intensive and practically unrealistic when the dimension is greater than 3. Therefore, it is important to automate the process of linearisation of the original nonlinear model. Based on the application of computer algebra, a constructive algorithm for the linearisation of a system of non-linear ordinary differential equations was developed. A software was developed on MatLab. The effectiveness of the proposed algorithm has been demonstrated on applied problems: an unmanned aerial vehicle dynamics model and a twolink robot model. The obtained linearized models were then used to test the stability of the original models. In order to account for possible inaccuracies in the measurements of the technical parameters of the model, an interval linearized model is adopted. For such a model, the procedure for constructing the corresponding interval characteristic polynomial and the corresponding Hurwitz matrix is automated. On the basis of the analysis of the properties of the main minors of the Hurwitz matrix, the stability of the studied system was analyzed. [ABSTRACT FROM AUTHOR]

This article describes the dynamical behavior of any linear control system on the group of proper motions SE(2). It characterizes the controllability property and the control sets of these systems. [ABSTRACT FROM AUTHOR]

This study deals with the controllability of multi-term fractional-order stochastic systems with impulsive effects and state-dependent delay that exhibit damping behavior. Based on fractional calculus theory, the Caputo fractional derivative is utilized to analyze the controllability of fractional-order systems. Mittag–Leffler functions and Laplace transform are used to derive the solution set of the problem. Sufficient conditions for the controllability of nonlinear systems are achieved using fixed-point techniques and stochastic theory. Finally, the results stated in the paper are validated using examples. [ABSTRACT FROM AUTHOR]

The primary focus of this article is to provide sufficient conditions for the controllability of Hilfer fractional neutral integrodifferential systems. By using the theories on fractional calculus, semigroup theory, and fixed point theorem method, the results are proved through integral contractors for the nonlinear neutral evolution equation in a non‐dense domain. In the end, the derived outcomes are validated through suitable illustrations. [ABSTRACT FROM AUTHOR]

The batch distillation is significant and flexible to separate liquid mixtures. However, it is usually energy intensive. The dividing‐wall column (DWC) is a promising and practical energy‐saving process intensification technology. The DWC for batch distillation (batch DWC) to separate benzene, toluene, and xylene mixtures was examined with composition and temperature control structures to verify its controllability. Besides, the batch DWC outperforms the conventional single‐column batch distillation and middle‐vessel batch distillation in terms of distillation time and energy consumption under the same conditions. In terms of more practical temperature control results, the batch DWC saves 63 % of energy compared with the conventional single‐column batch distillation and 47 % of energy compared with the middle‐vessel batch distillation. [ABSTRACT FROM AUTHOR]

In the present paper, we investigate the controllability, and observability of a non-homogeneous continuous-time fractal dynamical system (NC-TFDS). We show that the controllability is equivalent to a controllability matrix that has a full rank. We also show a relationship between controllability and fractal differential Lyapunov equation (F-DLE). We give some theorems for the observability of a NC-TFDS. Finally, we offer two examples are provided to illustrate the effectiveness of our results and compare it with the two papers Al-Zhour (2022) and (Sadek et al., 2022). [ABSTRACT FROM AUTHOR]

For a graph G we consider the problem of the existence of a switching equivalent signed graph with Laplacian eigenvalues that are all main and the problem of determination of all switching equivalent signed graphs with this spectral property. Using a computer search we confirm that apart from K 2 every connected graph with at most 7 vertices switches to at least one signed graph with the required property. This fails to hold for exactly 22 connected graphs with 8 vertices. If G is a cograph without repeated eigenvalues, then we give an iterative solution for the latter problem and the complete solution in the particular case when G is a threshold graph. The first problem is resolved positively for a particular class of chain graphs. The obtained results are applicable in control theory for generating controllable signed graphs based on Laplacian dynamics. [ABSTRACT FROM AUTHOR]

In this article, we examine a coupled system of fractional integrodifferential equations of Liouville–Caputo form with instantaneous impulsive conditions in a Banach space. We obtain the existence and uniqueness results by applying the theory of fixed point theorems. In a similar manner, we discuss Hyers–Ulam stability and controllability. We also present an example to show the validity of the obtained results. [ABSTRACT FROM AUTHOR]

The paper deals with the controllability properties of the Kawahara equation posed on a periodic domain. We show that the equation is exactly controllable by means of a control depending only on time and acting on the system through a given shape function in space. Firstly, the exact controllability property is established for the linearized system through a Fourier expansion of solutions and the analysis of a biorthogonal sequence to a family of complex exponential functions. Finally, the local controllability of the full system is derived by combining the analysis of the linearized system, a fixed point argument and some Bourgain smoothing properties of the Kawahara equation on a periodic domain. [ABSTRACT FROM AUTHOR]

In this work, we study the approximate controllability for retarded neutral differential equations with unbounded delay, non-instantaneous impulses, and non-local conditions. First, we set the problem in a natural Banach phase space satisfying Hale-Kato axiomatic Theory about the phase space for retarded ordinary equations with unbounded delay. Second, we assume some conditions on the nonlinear terms to achieve the approximate controllability using the technique developed by Bashirov and Ghahramanlou [6], which avoids the use of fixed point theorems. [ABSTRACT FROM AUTHOR]

Controlling the dynamics of chaotic systems is a task which is often addressed in an empirical way, particularly for placing sensors and actuators. Here, we show that selecting the measured variable and placing the actuator can be guided by considering the observability and controllability symbolic coefficients and applying the notion of flatness. This approach is here demonstrated on the piecewise linear Chua circuit, whose specific features are leveraged in constructing a discretized controller with a switch mechanism and optimally placed sensor and actuator. The feedback linearization is compared to a homogeneous and a passivity-based control laws, the flat control laws being more efficient than the others. It is thus shown that the proposed flat control law by feedback linearization is very efficient. The continuous time and discretized Chua circuit, governed by differential and difference equations, respectively, are treated. Most likely, these results could be extendable to a large group of natural and experimental systems. [ABSTRACT FROM AUTHOR]

We discuss the observability of a one-dimensional Schrödinger equation on certain time-dependent domain. In linear moving case, we give the exact boundary and pointwise internal observability for arbitrary time. For the general moving, we provide exact boundary observability when the curve satisfies some certain conditions. By duality theory, we establish the controllability of adjoint system. [ABSTRACT FROM AUTHOR]

The paper investigates the controllability of fractional descriptor linear systems with constant delays in control. The Caputo fractional derivative is considered. Using the Drazin inverse and the Laplace transform, a formula for solving of the matrix state equation is obtained. New criteria of relative controllability for Caputo’s fractional descriptor systems are formulated and proved. Both constrained and unconstrained controls are considered. To emphasize the importance of the theoretical studies, an application to electrical circuits is presented as a practical example. [ABSTRACT FROM AUTHOR]

This paper investigates the controllability and set controllability of periodically switched Boolean control networks (PSBCNs) via the semi-tensor product. Firstly, the algebraic form of switching signal is given and a parallel system is formed by combining the switching signal and the state. Then the controllability problem of PSBCNs is transformed into the set controllability problem of the new system, further, the criterion for controllability is obtained. Secondly, the set controllability matrix of PSBCNs is constructed, and the necessary and sufficient condition of set controllability for PSBCNs is presented. In addition, a more general PSBCN is considered and the criteria for its controllability and set controllability are proposed. Finally, a practical example is given to illustrate the obtained results, which shows that our new results are correct and effective. [ABSTRACT FROM AUTHOR]