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This paper investigates the identification of time-delay Boolean networks (TBNs) and time-delay Boolean control networks (TBCNs) via Cheng product. According to all admissible (input-)output sequences, definition on identifiability of the (TBCN) TBN is given. Two algorithms are designed to select suitable delay parameters of the TBN and TBCN, respectively. Based on these, the original systems are divided into several subsystems. Then by virtue of observability, the criteria for identifiability of the TBN and TBCN are obtained. Moreover, the corresponding constructing processes are presented to establish the internal structures of the TBN and TBCN. Finally, two illustrative examples are given to show the feasibility of the proposed methods. • Based on (input-)output data, definition on identifiability of TBNs(TBCNs) is given. • Two algorithms are designed to select suitable delay parameters of the TBN and TBCN. • By observability, the criteria for identifiability of the TBN and TBCN are obtained. • And the constructing processes are presented to establish the internal structures. [ABSTRACT FROM AUTHOR]

This paper investigates the approximate synchronization of singular logical networks (SLNs) using algebraic representations. Different from complete synchronization, which requires the state trajectories of the drive-response SLNs to be completely consistent after a finite time, approximate synchronization allows for admissible errors between the state trajectories of the drive-response SLNs. A definition of approximate synchronization for SLNs is proposed. By analyzing the constructed admissible matrices, the solvability of SLNs is discussed. A criterion is provided for the approximate synchronization of SLNs. Self-triggered control is then introduced to address the approximate synchronization of SLNs. Based on this, an algorithm is presented to design the self-triggered state feedback control of approximate synchronization. The method presented in this paper can significantly reduce updating frequencies of controllers. Finally, obtained theoretical results are illustrated through a genetic regulatory network. • A definition of approximate synchronization for singular logical networks is proposed. Approximate synchronization is more general and has wider applications than complete synchronization. • A criterion for the approximate synchronization of singular logical networks is provided. The method proposed in this paper is more effective than existing results. • An algorithm for designing self-triggered state feedback control of approximate synchronization is presented. The method proposed in this paper can significantly reduce updating frequencies of controllers. [ABSTRACT FROM AUTHOR]

This paper focuses on admissibility analysis and stabilization for neutral descriptor hybrid systems (NDHSs) with time-varying delays. The main object is to design mode dependent state feedback controller (SFC) and realize admissibility and stabilization of the NDHSs. Sufficient conditions are provided in terms of linear matrix inequalities (LMIs) via constructing integrated L-K functional. Two simulation examples including a partial element equivalent circuit (PEEC) model are used to testify the validity and practicality of the proposed method. [ABSTRACT FROM AUTHOR]

• The reduced state transition matrix of Boolean (control) networks is introduced to analyze the disturbance decoupling problem. • The relationship between three types of disturbance decoupling and robust indistinguishability is revealed. • Algebraic conditions with lower computational complexity are given for disturbance decoupling. Disturbances are ubiquitous and affect the normal operation of systems. This paper investigates the disturbance decoupling problem of Boolean networks (BNs) and Boolean control networks (BCNs) by a robust indistinguishability method. Utilizing a new method based on the reduced state transition matrix, the relationship between three types of disturbance decoupling and robust indistinguishability is revealed, which also builds a link between robust observability and disturbance decoupling. Based on a parameter extraction mapping, several feasible criteria are presented for original and weak disturbance decoupling of BNs and BCNs. Additionally, our approach is more concise and has a lower computational complexity than the existing methods. Finally, two examples are presented to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Stabilizability analysis and stabilizable switching signals design of switched Boolean networks (SBNs) are further investigated via semi-tensor product of matrices in this paper. First, two kinds of stabilizability of SBNs, stabilizability under arbitrary switching signals and pointwise stabilizability, are discussed under the framework of an improved approach. Second, more general stable structures, kernel attractors, are defined and studied. Subsequently, several necessary and sufficient conditions are derived to ascertain that an SBN is stabilizable under arbitrary switching signals or pointwise stabilizable to a kernel attractor. Then a constructive method is presented to determine all stabilizable switching signals dependent on states (SSDSs), which drive the considered network stabilizable to a fixed point, a kernel attractor or a set. Finally, two examples are given to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is intended to study output feedback-based H ∞ admissibilization for singular Markovian jump time-varying delays systems via Moore–Penrose generalized inversion technique. The main aim is to design singular dynamic compensator based on output feedback control idea and Moore–Penrose generalized inversion technique, such that the time-varying delays singular Markovian jump system realizes not only stochastic stability, but also regularity, impulse-freeness (which are collectively known as stochastic admissibility) and achieves H ∞ interference level. Time delay-dependent and mode-dependent L–K candidate functional is constructed, Moore–Penrose generalized inversion technique is utilized, then the improved H ∞ admissibilization conditions for singular Markovian jump time-varying delays systems are provided by virtue of linear matrix inequalities. Simulation examples including a direct current motor-controlled inverted pendulum system are employed to confirm the effectiveness and practicability of the addressed singular dynamic compensation technique. [ABSTRACT FROM AUTHOR]

The α -exponential stability analysis and l 1 controller synthesis of positive Takagi–Sugeno fuzzy discrete-time systems with time-varying delays are discussed in this paper. A sufficient condition of α -exponential stability for autonomous positive fuzzy systems is first established by constructing a new Lyapunov–Krasovskii functional, which depends on a given scalar 0 < α < 1 and the bound of time-varying delays. Then, a sufficient condition for controlled systems with l 1 gain constraint is also presented while imposing α -exponential stability, upon which, a constrained l 1 controller is designed for both single-input and multi-input cases. Finally, an example is given to show the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

The norm properties of Lyapunov mappings and their restrictions on symmetric and skew-symmetric subspaces are investigated. For non-negative, non-positive, and tridiagonal matrices, this paper gives an affirmative answer to an open conjecture which says that the norm of a Lyapunov mapping over the space of real square matrices equals that of its restricted map over the subspace of real symmetric matrices. In addition, matrix transformation and norm relationships on certain matrices arising from the Lyapunov mapping and its restrictions are provided. [ABSTRACT FROM AUTHOR]

This paper considers the impacts on attractors of function perturbations in Boolean networks via semi-tensor product of matrices. Two types of function perturbations: one-bit perturbation and modifications of update schedule, are investigated. First, the algebraic form of perturbed Boolean networks under one-bit perturbation is given, based on which several necessary and sufficient conditions of different kinds of effects on state transition and attractors are obtained. Besides, a Boolean network with update schedule is studied and the definition of its adjacent diagraph is first presented in this paper. Furthermore, transition matrix of the updated network is calculated to analyze the changes of fixed points and limit cycles. At last, identifying function perturbations with its application in a Drosophila melanogaster segmentation polarity gene network is shown to demonstrate the practicability and effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Network synchronization, explicating typical collective behaviors of coupled systems, plays a crucial role in social production and life. This paper addresses the synchronization problem of drive–response singular Boolean networks (SBNs). The solvability of drive–response SBNs is investigated based on the matrix representation. In view of the existence and uniqueness of the solutions to drive–response SBNs, three types of concepts, synchronization, strong synchronization and weak synchronization, are put forward for the first time. By two new systems, a restricted BN and a switched restricted BN, which are constructed from the considered systems, several synchronization conditions are provided to deal with the circumstances of unique solutions and multiple solutions, respectively. Besides, the synchronous ratio is defined to characterize the synchronization capability of drive–response SBNs for the case of multiple solutions. Finally, several examples are given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Abstract: We introduce two kinds of sums of Kronecker products, and their induced operators. We study the algebraic properties of these two kinds of matrices and their associated operators; the properties include their eigenvalues, their eigenvectors, and the relationships between their spectral radii or spectral abscissae. Furthermore, two projected matrices of these Kronecker products and their induced operators are also studied. [Copyright &y& Elsevier]

Abstract: This paper considers the problem of robust stability analysis of Cohen–Grossberg neural networks with time-varying delays and norm-bounded parameter uncertainties. The activation functions are assumed to be bounded and globally Lipschitz continuous. Both the monotonic increasing and non-monotonic increasing activations are considered. In terms of linear matrix inequalities (LMIs), sufficient conditions are obtained by using the Lyapunov–Krasovskii method, which guarantee the existence, uniqueness and global robust asymptotic stability of the equilibrium point of the delayed Cohen–Grossberg neural network. It is theoretically established that the derived LMI conditions are less conservative than certain existing ones in the literature. Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions. [Copyright &y& Elsevier]

This paper investigates the set stability of probabilistic Boolean networks (PBNs) with switching topology. To deal with this problem, two novel concepts, set reachability and the largest invariant set family, are defined. By constructing an auxiliary system, the necessary and sufficient conditions for verifying set reachability are given and the calculation method for the largest invariant set family is obtained. Based on these two results, an equivalent condition of set stability is derived, which can be used to determine whether a PBN with switching topology can be stabilized to a given set. In addition, the design method of switching signal is proposed by combining the characteristic of the largest invariant set family, and a numerical example is reported to demonstrate the efficiency of presented approach. [ABSTRACT FROM AUTHOR]

This study discusses the robust stability problem of Boolean networks (BNs) with data loss and disturbances, where data loss is appropriately described by random Bernoulli distribution sequences. Firstly, a BN with data loss and disturbances is converted into an algebraic form via the semi-tensor product (STP) technique. Accordingly, the original system is constructed as a probabilistic augmented system, based on which the problem of stability with probability one for the original system becomes a set stability with probability one for the augmented system. Subsequently, certain criteria are proposed for the robust stability of the systems. Moreover, an algorithm is developed to verify the robust set stability of the augmented system based on truth matrices. Finally, the validity of the obtained results is demonstrated by an illustrative example. [ABSTRACT FROM AUTHOR]

• The set stabilization problem of Markovian jump Boolean control networks by semi tensor product is studied. • A necessary and sufficient criterion for the feedback set stabilization of Markovian jump Boolean control networks is proposed based on average optimal control problem. • A policy iterati algorithm for set stabilization problem is deduced, based on which, the state feedback control is designed. In this paper, the authors address the set stabilization problem for Markovian jump Boolean control networks (MJBCNs) by state feedback control. Based on the semi-tensor product, a necessary and sufficient condition for the set stabilization of MJBCNs is put forward via optimal control approach. Moreover, a policy iterative algorithm is deduced for designing the state feedback control. Finally, the proposed method and results are supported by the example of an apoptosis network. [ABSTRACT FROM AUTHOR]

Stabilization and set stabilization of switched Boolean control networks are investigated by using flipping mechanism in this paper. Firstly, with the help of Warshall algorithm, an explicit criterion for the stabilization of switched Boolean control networks is derived. Secondly, the necessary and sufficient condition for the solvability of stabilization of switched Boolean control networks, by flipping some elements of perturbation set once, is presented. Thirdly, a search algorithm is proposed to calculate the minimum number of stabilization flipped nodes and what exactly they are. Furthermore, a necessary and sufficient condition is established for the solvability of set stabilization of switched Boolean control networks by flipping some elements of perturbation set once. Analogously, an algorithm is given to find the minimum number of set stabilization flipped nodes. Finally, examples are shown to demonstrate the feasibility of the above results. • An explicit criterion for the stabilization of switched Boolean control networks is derived. • Necessary and sufficient condition for the stabilization of switched Boolean control networks, by flipping some elements of perturbation set once, is presented. • A search algorithm is proposed to calculate the minimum number of stabilization flipped nodes and what exactly they are. • A necessary and sufficient condition is established for the set stabilization of switched Boolean control networks by flipping some elements of perturbation set once. • An algorithm is given to find the minimum number of set stabilization flipped nodes. [ABSTRACT FROM AUTHOR]

• Compared with the existing results, an improved algorithm which can effectively reduce computational complexity of calculating the maximum control invariant set is given. • An explicit criterion is derived to check whether a switched Boolean network satisfies set stabilization. • An event-triggered mechanism is formulated in the process of designing time-varying set stabilization state feedback controller. • A systematic procedure is devised to design event-triggered set stabilization state feedback controller of switched Boolean networks. • A method is proposed to obtain all possible event-triggered state feedback controllers for set stabilization of switched Boolean networks. In this paper, the set stabilization problem of switched Boolean networks is reinvestigated. An event-triggered mechanism is formulated in the process of designing time-varying set stabilization state feedback controller. First, compared with the existing results, an improved algorithm which can effectively reduce computational complexity of calculating the maximum control invariant set is given. Second, using Warshall algorithm, an explicit criterion is derived to check whether a switched Boolean network satisfies set stabilization. Third, a systematic procedure is devised to design event-triggered set stabilization state feedback controller of switched Boolean networks. Then, a method is proposed to obtain all possible event-triggered state feedback controllers for set stabilization of switched Boolean networks. Finally, two examples are shown to demonstrate the effectiveness of presented results. [ABSTRACT FROM AUTHOR]

This paper introduces the detectability notions and investigates the detectability properties for Boolean networks (BNs) and Boolean control networks (BCNs). A BN (BCN) possesses the property of detectability if the current state can be determined by limited observed data. According to different situations, three types of detectabilities are defined: strong detectability, detectability and weak detectability. Firstly, using the semi-tensor product of matrices, the BCN is written as an equivalent algebraic expression, which is called the data form. Secondly, some criterion and detection algorithms are provided for checking detectabilities via this novel form. Thirdly, four types of properties: stability, stabilizability, observability and detectability, are compared and analyzed, and then their relationships are clearly described in two diagrams, which provide a new perspective to analyze the characterization of BNs and BCNs. Finally, for better presentation, two practical examples are presented to show the effectiveness of the obtained new results. [ABSTRACT FROM AUTHOR]

In this paper, two kinds of stabilizability of switched Boolean networks (SBNs), consistent stabilizability and stabilizability under time-varying output feedback (TVOF), are investigated on the basis of adjoint logical networks (ALNs), which are constructed via switching signals. Firstly, globally consistent stabilizability of SBNs is equivalently converted into local (one state) pointwise stabilizability of ALNs, under which all suitable finite-time switching signals can be designed. Then the method is generalized to design stabilizable TVOF switching signals. Finally, to show the effectiveness of obtained results, two types of stabilizability of a shift register are discussed. [ABSTRACT FROM AUTHOR]