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Group consensus implies reaching multiple groups where agents belonging to the same cluster reach state consensus. This article focuses on linear multiagent systems under nonnegative directed graphs. A new necessary and sufficient condition for ensuring group consensus is derived, which requires the spanning forest of the underlying directed graph and that of its quotient graph induced with respect to a clustering partition to contain equal minimum number of directed trees. This condition is further shown to be equivalent to containing cluster spanning trees, a commonly used topology for the underlying graph in the literature. Under a designed controller gain, lower bound of the overall coupling strength for achieving group consensus is specified. Moreover, the pattern of the multiple consensus states formed by all clusters is characterized when the overall coupling strength is large enough. [ABSTRACT FROM AUTHOR]

This article investigates the stealthy false data injection attack design problem for a class of cyber physical systems equipped with state estimators and attack detectors. The objective is to worsen the estimation performance without triggering any alarm. First, a necessary and sufficient condition for the existence of perfect attacks, which alter the state estimate without affecting residual signals, is provided. It is shown that the estimation error can be arbitrarily large under the well-designed perfect attacks. Second, if the perfect attacks do not exist, the existence of nonperfect attacks, which worsen the estimation performance with a degree influence on residual signals, is analyzed. It is shown that the desired nonperfect attack sequence can be designed by analyzing the maximum eigenvalue and the corresponding eigenvector of an auxiliary matrix. Compared with the existing methods, in this article, attacks are designed without knowledge of estimators and can be injected from any time point. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

The discrete distributed observer is developed recently to solve the cooperative output regulation problem. The validation of the existing discrete distributed observer depends on the establishment of the communication network. In some practical applications, only the sensor network can be established among all agents. To handle such cases, we propose a sensory feedback-based discrete distributed observer, which depends on the relative output of neighboring agents. In contrast to existing results, the design of the discrete distributed observer and cooperative output regulation analysis should be conducted simultaneously. Resorting to the small-gain theorem, we develop a small-gain condition-based approach and a low-gain-based approach, respectively. By these two approaches, we demonstrate that the discrete distributed observer holds and the cooperative output regulation problem of heterogeneous discrete-time linear multiagent systems can be solved. [ABSTRACT FROM AUTHOR]

This technical note investigates the positive consensus problem of multiagent systems with directed communication topologies, where all the agents have identical continuous-time positive linear dynamics. Existing works of such a problem mainly focus on the case, where networked communication topologies are of either undirected and incomplete graphs, or strongly connected directed graphs. In contrast to them, we study this problem in which the communication topologies of the multiagent system are described by directed graphs each containing a spanning tree, which is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains. Based on the existing results in spectral graph theory and positive linear systems theory, several necessary, and sufficient conditions on positive consensus of the directed multiagent system are derived through using linear matrix inequality techniques. A primal-dual iterative algorithm is developed for the computation of solutions. Finally, several numerical simulations are provided to illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this article, we investigate the robust stabilization of linear time-invariant (LTI) systems with external disturbances via event-triggered impulsive control (ETIC). Especially, in order to suppress the disturbances effectively, the impulsive instant sequence is generated through the sliding-variable-based event-triggering mechanism (ETM). Based on the proposed ETM, some sufficient conditions are derived to ensure the robust stabilization of the LTI systems and to exclude Zeno phenomenon. It is shown that the system states are ultimately bounded under the ETIC, and the ultimate bound can be arbitrarily small by selecting the appropriate parameter of ETM. More interestingly, it is proved that our obtained results can well deal with the case of unknown bounded external disturbances, which is often addressed by the adaptive control in the previous results. Then, the theoretical results are applied to the motor servo systems in the presence of external disturbances. Finally, two illustrative examples are presented to show the validity of the results. [ABSTRACT FROM AUTHOR]

This article investigates the cluster consensus control problem for general linear multiagent systems. The focus of this article is especially to solve the following problem: in what kinds of connection scenarios can agents achieve cluster consensus regardless of the coupling strength (CCRCS). Different from existing literature, this article extends the case to general partition graphs, including both acyclic and cyclic partition cases. New analysis methods are put forward. It is proved that, under some basic assumptions, the multiagent systems can achieve CCRCS if and only if the interaction topology satisfies the nonvicious circle condition, which is proposed for the first time. An algorithm is presented which can check whether a given interaction topology satisfies the nonvicious circle condition. The result can also be extended to heterogeneous cases that agents from different clusters possess nonidentical system dynamics. [ABSTRACT FROM AUTHOR]

Distributed event- and self-triggered controllers are developed for approximate leader-follower consensus with robustness to adversarial Byzantine agents for a class of homogeneous multi-agent systems (MASs). A strategy is developed for each agent to detect Byzantine agent behaviors within their neighbor set and then selectively disregard their transmission. Selectively removing Byzantine agents results in time-varying discontinuous changes to the network topology. Nonsmooth dynamics also result from the use of event/self-triggered strategies and triggering condition estimators that enable intermittent communication. Nonsmooth Lyapunov methods are used to prove approximate consensus of the MAS consisting of the remaining cooperative agents. Simulations are included to validate the result and to outline the tradeoff between communication and performance. [ABSTRACT FROM AUTHOR]

This article studies controllability of a discrete-time linear dynamical system using nonnegative and sparse inputs. These constraints on the control input arise naturally in many real-life systems, where the external influence on the system is unidirectional, and activating each input node adds to the cost of control. We derive the necessary and sufficient conditions for the controllability of the system, without imposing any constraints on the system matrices. Unlike the straightforward extension of the well-known Kalman-rank-based controllability criteria, the conditions presented in this article can be verified in polynomial time. The verification complexity of our conditions is independent of the sparsity level. Our results also provide a closed-form expression for the minimum number of control nodes to be activated at every time instant to ensure controllability of the system using nonnegative controls. Furthermore, for the systems satisfying the derived controllability conditions, we provide approximate algorithms that solve for the nonnegative inputs. [ABSTRACT FROM AUTHOR]

It is well known that the “fixed spectrum” (i.e., the set of fixed modes) of a multichannel linear system plays a central role in the stabilization of such a system with decentralized control. A parameterized multichannel linear system is said to be “structurally complete” if it has no fixed spectrum for almost all parameter values. Necessary and sufficient algebraic conditions are presented for a multichannel linear system with dependent parameters to be structurally complete. An equivalent graphical condition is also given for a certain type of parameterization. [ABSTRACT FROM AUTHOR]

Strictly unstable linear systems under additive and nonvanishing stochastic noise with unbounded supports are known to be impossible to stabilize by using deterministically constrained control inputs. In this article, similar impossibility results are obtained for the scenarios where the control input is probabilistically constrained and the support of the noise distribution is not necessarily unbounded. In particular, control policies that have bounded time-averaged second moments are considered. It is shown that for such control policies, there are critical average moment bounds, below which second moment stabilization of a linear stochastic system is not possible, and moreover, second moment of the state diverges regardless of the choice of control policy and the initial state distribution. Nonnegative-definite Hermitian matrices are exploited to extract sufficient instability conditions that can be assessed by using the eigenstructure of the system matrix and the distribution of the noise. The results indicate that in certain networked control system settings with noise, designing stabilizing constrained controllers is an impossible task, if the probability of successful transmissions of control commands over the network is known to be too small in average. [ABSTRACT FROM AUTHOR]

Modal participation factors are widely used in the power industry and other applied areas. Hashlamoun, Hassouneh, and Abed (2009) observed that the definition of state-in-mode participation factors (SIMPFs) commonly used in the modal analysis of linear systems could lead to inadequate results. Accordingly, they proposed an alternative definition of SIMPFs. This article uncovered a weakness in their formulation in that it yields results highly sensitive to varying eigenvector normalizations for complex eigenvalues. Thus, we present a modified well-defined formulation and interpretation of SIMPFs in this article. The proposed approach combines the framework of averaging over an uncertain set of initial conditions, introduced by Hashlamoun, Hassouneh, and Abed, with the novel concept of modal energy. Following this approach, an alternative definition for mode-in-state participation factors was discovered, which differs from the conventional definition. Simple examples are used to show that new definitions provide more accurate measures of state-in-mode and mode-in-state participations compared to conventional participation factors in the case of an arbitrary distribution of initial conditions over state variables. In particular, the proposed energy-based interpretation of novel indicators precludes negative or complex measures. [ABSTRACT FROM AUTHOR]

An intermittent feedback-based control policy is proposed for rejecting bounded disturbance signals in a continuous, linear time-invariant (LTI) system with distinct and rational eigenvalues. The proposed policy maximizes the average feedback-off time while retaining the state trajectory inside a prespecified safe region. To achieve this, the feedback link is alternatively turned on and off. During feedback-on intervals, the state trajectory is steered to the origin in min–max time and then feedback is turned off for some maximal precomputed duration. The largest subset of the safe region that is invariant under the proposed policy is characterized. The feedback control and the open-loop control in the proposed policy, which are applied during feedback-on and feedback-off intervals, respectively, are obtained by solving certain min–max and max–min time-optimal control problems. It is shown that the proposed policy achieves the abovementioned objective of maximizing the average feedback-off time. An interesting additional feature of this policy is that the optimal control problems in it need to be solved only once offline and, hence, they do not increase the burden of real-time computation. [ABSTRACT FROM AUTHOR]

A solution is presented to a long-standing open problem of control theory, the decoupling of linear systems using static-state feedback while assuring stability. Both diagonal and block decoupling is considered. The earliest known investigation of system decoupling dates back to 1934 and all past stable solutions were obtained under restrictive assumptions on system, block structure, or on a particular form of the control law. Most often, the results were limited to regular state feedback. The present formulation avoids restrictive hypotheses. The system is stabilized first and then decoupled while preserving stability. The existence of decoupling feedback is conditioned by system invariants with respect to the group of stability-preserving decoupling transformations. Since nonregular state feedback is authorized, some well-known results of regular decoupling are not retained. In particular, the presence of interconnection zeros does not prevent a stable decoupling to be achievable. [ABSTRACT FROM AUTHOR]

For a linear time varying (LTV) system containing stable and unstable modes, this article gives the necessary and sufficient conditions for asymptotic decoupling of stable modes. Establishment of the conditions relies on newly developed techniques for analyzing matrix exponential and state transition matrix. The research exploits fundamental properties of LTV systems and advances the knowledge base of linear control theory. The results can find a direct application in the autonomous synchronization problem for heterogeneous multiagent systems. The research methodology is based on rigorous theoretical proofs and numerical verification. [ABSTRACT FROM AUTHOR]

The problem of output tracking is addressed in this article by a reformulation in terms of a two-point boundary value problem for the plant's zero dynamics, which is allowed to be unstable. On this basis, a hybrid feedback regulator ensuring output tracking is then designed. The robustness properties of the proposed regulator as well as connections with periodic (cheap) optimal control, output regulation, and possible extensions to the nonlinear setting are also discussed. [ABSTRACT FROM AUTHOR]

This article studies the constrained switching (linear) system which is a discrete-time switched linear system whose switching sequences are constrained by a deterministic finite automaton. The stability of a constrained switching system is characterized by its constrained joint spectral radius that is known to be difficult to compute or approximate. Using the semitensor product of matrices, the matrix-form expression of a constrained switching system is shown to be equivalent to that of a lifted arbitrary switching system. Then, the constrained joint/generalized spectral radius of a constrained switching system is proven to be equal to the joint/generalized spectral radius of its lifted arbitrary switching system which can be approximated by off-the-shelf algorithms. [ABSTRACT FROM AUTHOR]

In this article, uncertain continuous-time and discrete-time linear time-invariant systems are considered. The uncertainties are assumed to affect polynomially the dynamics of the system and they can be structured. The problem of computing the distance to internal instability of an internally exponentially stable nominal system is solved by using tools from algebraic geometry, thus extending previous results valid in case of unstructured uncertainties. The choice of the nominal system is formulated and solved as the choice of a point in the parameter space that is sufficiently far from the boundary of the domain of stability. A simple example of application to robust control is outlined. [ABSTRACT FROM AUTHOR]

This article systematically studies consensus of linear multiagent systems (MASs) on directed graphs through adaptive event-triggered control. It presents innovative adaptive event-triggered state-feedback protocols with novel composite event-triggering conditions. Two specific designs in terms of different event-triggering conditions and laws of adaption are first discussed for linear MASs on strongly connected directed graphs, which are then extended to general directed graphs that contain a spanning tree. Moreover, another adaptive event-triggered protocol is proposed for solving leader–follower consensus that tracks a leader of a bounded control input. The protocols inherit the merits of both adaptive control and event-triggered control: the protocols can be implemented in a fully distributed way, since the Laplacian is avoided in design, and each agent only needs to know the relative information between neighbors at discrete instants determined by event-triggering conditions. Compared with the existing related results, the proposed protocols are applicable for linear MASs on general directed graphs, and moreover, the time-dependent term in the event-triggering conditions is allowed to be a class of positive L1 functions. Two numerical examples clearly verify the effectiveness of the proposed protocols. [ABSTRACT FROM AUTHOR]

In this article, we first establish an exponential stability result for a class of linear switched systems and then apply this result to show the existence of the distributed observer for a discrete-time leader system over jointly connected switching networks. Then, we further develop the adaptive distributed observer for the discrete-time leader system over jointly connected switching networks, which has the advantage over the distributed observer in that, it does not require that every follower subsystem know the system matrix of the leader system. As an application of the discrete-time distributed observer, we solve the cooperative output regulation problem of a discrete-time linear multiagent system over jointly connected switching networks. A leader-following formation problem of mobile robots is used to illustrate our design. [ABSTRACT FROM AUTHOR]

Due to their relevance in controller design, we consider the problem of determining the L2-gain, passivity properties, and conic relations of an input–output system. While, in practice, the input–output relation is often undisclosed, input–output data tuples can be sampled by performing (numerical) experiments. Hence, we present sampling strategies for discrete time and continuous time linear time-invariant systems to iteratively determine the L2-gain, the shortage of passivity and the cone with minimal radius that the input–output relation is confined to. These sampling strategies are based on gradient dynamical systems and saddle point flows to solve the reformulated optimization problems, where the gradients can be evaluated from only input–output data samples. This leads us to evolution equations, whose convergence properties are then discussed in continuous time and discrete time. [ABSTRACT FROM AUTHOR]

This article investigates the cooperative output regulation problem for heterogeneous linear multiagent systems by event-triggered control, where the system matrix of the exosystem is not available to all agents. First, an event-triggered adaptive distributed observer is designed for each agent to estimate both the state and the system matrix of the exosystem. Then, a fully distributed event-triggered dynamic output feedback control law is proposed for each agent. Meanwhile, a fully distributed event-triggering mechanism is proposed such that each agent can determine when to broadcast its information to its neighbors. It is shown that with the proposed event-triggered control strategy, the cooperative output regulation problem is solved by intermittent communication in a fully distributed manner in the sense that no global information, such as the eigenvalues of the Laplacian matrix or the number of the agents, is used. It is also shown that Zeno behavior is excluded for each agent. Finally, a numerical example is given to illustrate the effectiveness of the proposed event-triggered control strategy. [ABSTRACT FROM AUTHOR]

Recent results have shown that, for continuous-time systems obtained by cascading an asymptotically stable system with an inner system, the first n Hankel singular values are greater than or equal to those of the original system. Similarly, cascading a system in minimal form with an inner system, the same property holds for the linear quadratic Gaussian (LQG) characteristic values. In this article, we consider the discrete-time case and demonstrate that the property also holds for these systems. A very important consequence stemming from these results is that the Hankel singular values and the LQG characteristic values of input-delayed discrete systems are greater than or equal to those of their zero-delay counterpart. [ABSTRACT FROM AUTHOR]

Motivated by challenges in feedback control with event-triggered control input updates, this article studies an ellipsoidal set-valued feedback control problem for linear time-invariant (LTI) discrete-time (DT) systems, and its application to event-triggered control systems. First, a state feedback controller based on the set-valued information is designed for LTI DT systems with disturbances. Then, the stability of the closed-loop system is analyzed, and the state of the closed-loop system is shown to be uniformly ultimately bounded in an ellipsoidal set. Based on the proposed set-valued feedback controller, we consider the case when the event-triggering condition (ETC) is described by an ellipsoidal set for an event-triggered control system. To ensure the requirements on control performance and communication rates simultaneously, an optimal ETC design problem is formulated and its optimal solution is provided. Finally, simulation examples are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article studies the parameter tuning problem of positive linear systems for optimizing their stability properties. We specifically show that, under certain regularity assumptions on the parameterization, the problem of finding the minimum-cost parameters that achieve a given requirement on a system norm reduces to a geometric program, which, in turn, can be exactly and efficiently solved by convex optimization. The flexibility of geometric programming allows the state, input, and output matrices of the system to simultaneously depend on the parameters to be tuned. The class of system norms under consideration includes the H2 norm, H∞ norm, Hankel norm, and Schatten p-norm. Also, the parameter tuning problem for ensuring the robust stability of the system under structural uncertainties is shown to be solved by geometric programming. The proposed optimization framework is further extended to delayed positive linear systems, where it is shown that the parameter tuning problem jointly constrained by the exponential decay rate, the L1-gain, and the L∞-gain can be solved by convex optimization. The assumption on the system parameterization is stated in terms of posynomial functions, which form a broad class of functions and thus allow us to deal with various interesting positive linear systems arising from, for example, dynamical buffer networks and epidemic spreading processes. We present numerical examples to illustrate the effectiveness of the proposed optimization framework. [ABSTRACT FROM AUTHOR]

This article is a comprehensive study of a long-observed phenomenon of increase in the stability margin and so the rate of convergence of a class of linear systems due to time delay. We use the Lambert W function to determine: 1) in what systems the delay can lead to increase in the rate of convergence; 2) the exact range of time delay, for which the rate of convergence is greater than that of the delay-free system; and 3) an estimate on the value of the delay that leads to the maximum rate of convergence. For the special case when the system matrix eigenvalues are all negative real numbers, we expand our results to show that the rate of convergence in the presence of delay depends only on the eigenvalues with minimum and maximum real parts. Moreover, we determine the exact value of the maximum rate of convergence and the corresponding maximizing time delay. We demonstrate our results through a numerical example on the practical application in accelerating an agreement algorithm for networked systems by using a delayed feedback. [ABSTRACT FROM AUTHOR]

Although passivity has been proven to be quite useful, it excludes a majority of dynamic systems in applications, and typically, the property cannot be preserved through discretization. To overcome these shortcomings, the class of passivity-short (PS) systems is investigated in this article, and canonical forms are derived in both continuous-time and discrete-time domains. Explicit conditions are found to guarantee the PS property through discretizing PS/non-PS systems and, for those that do not satisfy the conditions, two designs of output feedback controls are presented to make sampled-data systems PS, regardless of the PS property of original continuous-time systems. One of the designs is in the discrete-time domain, and the other is in the continuous-time domain. The control design to ensure the PS property in the continuous-time domain is also developed. These results provide a full description of PS systems in both domains as well as their relationship through discretization. [ABSTRACT FROM AUTHOR]

The notions of eigenvalue, pole and moment at a pole of a continuous-time, nonlinear, time-invariant system are studied. Eigenvalues and poles are first characterized in terms of invariant subspaces. Tools from geometric control theory are used to define nonlinear enhancements of these notions and to study their relationship with the solution of certain partial differential equations, cascade decompositions and steady-state impulse responses. The theory is illustrated by means of worked-out examples and its significance is demonstrated by solving the model reduction problem by moment matching at poles for nonlinear systems. [ABSTRACT FROM AUTHOR]

In this paper, we study incremental stability of monotone nonlinear systems through contraction analysis. We provide sufficient conditions for incremental asymptotic stability in terms of the Lie derivatives of differential one-forms or Lie brackets of vector fields. These conditions can be viewed as sum- or max-separable conditions, respectively. For incremental exponential stability, we show that the existence of such separable functions is both necessary and sufficient under standard assumptions for the converse Lyapunov theorem of exponential stability. As a by-product, we also provide necessary and sufficient conditions for exponential stability of positive linear time-varying systems. The results are illustrated through examples. [ABSTRACT FROM AUTHOR]

In this article, we consider the sampled-data leader-following consensus problem for a class of general linear multiagent systems over both static directed networks and switching directed networks. A distributed asynchronous sampled-data state feedback control law is proposed. We show by Lyapunov analysis that the problem can be solved by the proposed control law as long as the sampling periods of all agents are smaller than a given threshold, which can be explicitly calculated. An example is given to illustrate the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

This paper presents a novel method to compute the distance to instability for linear time-invariant delay systems with multiple delays, subjected to combined uncertainties on the system matrices and the delay parameters. The method is able to fully exploit structure and possible interdependencies between the uncertainties affecting the coefficient matrices, the property that realistic perturbations are real valued, and the structure of the delay equation. The resulting algorithm relies on a characterization in terms of the pseudospectral abscissa and on techniques from optimization over manifolds of matrices. [ABSTRACT FROM AUTHOR]

This paper considers an iterative procedure to design a minimum possible order unknown input functional observer for linear time-invariant systems. Necessary and sufficient conditions for the existence of the observer are given. The proposed procedure is simple and is based neither on the solution of a generalized Sylvester equation nor canonical forms. This procedure can be easily implemented due to its incremental form. The main feature of our procedure is then the simplicity of the design. Moreover, in the case of a single functional to be observed, a minimum order stable linear unknown input functional observer is obtained. [ABSTRACT FROM AUTHOR]

This paper considers the consensus problem of linear multiagent systems with distributed infinite transmission delays. A novel low gain controller is proposed and it is shown that the proposed controller can solve the consensus problem if the open loop agent dynamics have no exponentially unstable eigenvalues and the communication topology is fixed and contains a spanning tree. One of the distinctive advantages of the proposed controller is that it does not require the knowledge of transmission delays. Our proofs are established based on a stability result on infinite delays, which can be seen as an extension of the commonly used frequency domain method. Our results include those results on distributed bounded delays and constant delays as their special cases. Simulation examples are provided to illustrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

In this paper, new properties of the cascade between a multi-input multi-output linear time-invariant system, referred to in the following as the original system, and an inner system are dealt with. In particular, attention is devoted to the relationship between the Hankel singular values and characteristic values of the cascade system and those of the original one, proving that, if the inner system has gain greater than or equal to one, then the first $n$ Hankel singular values (characteristic values) of the cascade system are greater than or equal to those of the original system. The results are then applied to derive a new property of minimum phase systems. [ABSTRACT FROM AUTHOR]

This paper studies the consensusability problem of multiagent systems (MASs), where agents communicate with each other through Markovian packet loss channels. We try to determine conditions under which there exists a linear distributed consensus controller such that the MAS can achieve mean square consensus. We first provide a necessary and sufficient consensus condition for MASs with single input and independent and identically distributed channel losses, which complements existing results. Then, we proceed to study the case with identical Markovian packet losses. A necessary and sufficient consensus condition is first derived based on the stability of Markov jump linear systems. Then, a numerically verifiable consensus criterion in terms of the feasibility of linear matrix inequalities (LMIs) is proposed. Furthermore, analytic sufficient conditions and necessary conditions for mean square consensusability are provided for general MASs. The case with nonidentical packet loss is studied subsequently. The necessary and sufficient consensus condition and a sufficient consensus condition in terms of LMIs are proposed. In the end, numerical simulations are conducted to verify the derived results. [ABSTRACT FROM AUTHOR]

This paper studies the distributed event-triggered tracking control problem of general linear multiagent systems with a dynamic leader, whose control input might be nonzero and unknown. The existence of the leader's unknown input renders the network heterogeneous and largely increases the difficulty of designing distributed event-based protocols. To solve this problem, we establish a novel asynchronous edge-based event-triggered mechanism, under which communication is not required from the leader to its out-neighbors (informed followers) or by the edge, unless the embedded triggering functions are triggered. Using this mechanism, we design a static asynchronous edge-based event-triggered protocol and an adaptive one, both of which guarantee the achievement of the leader–follower consensus and the exclusion of the Zeno behavior. Note that the adaptive event-based protocol is fully distributed, requiring no global information of the network topology, such as the network's scale, the smallest nonzero eigenvalue of the Laplacian matrix, and the upper bound of the leader's control input. [ABSTRACT FROM AUTHOR]

The minimal positive realization of externally positive systems is still an open problem due to various restrictions caused by the nonnegativity constraint on the state-space matrices. In this paper, the minimal strongly eventually positive realization, which relaxes the nonnegativity constraint on the state-space model and only requires that the state trajectory is nonnegative after a certain number of steps, is proposed for an externally positive system. It is shown that a discrete-time transfer function with a simple strictly dominant root is externally positive if and only if it has a minimal strongly eventually positive realization. A constructive proof is provided. The continuous-time counterpart is also addressed by transforming it into a corresponding discrete-time case. [ABSTRACT FROM AUTHOR]

A new necessary and sufficient condition for the controllability of networked linear time-invariant systems is derived, where the network topology is general and the nodes have identical higher dimensional dynamics. The condition is easier to verify, explicitly illustrating how the network topology, node-system dynamics, external control inputs, and inner interactions altogether affect the controllability of the whole networked system. Furthermore, the controllability of the specified Cartesian product networks is revisited, revealing that the necessity of the controllability criterion established in the work presented by Chapman et al., does not hold. In view of this, a modified, necessary, and sufficient condition is established. The effectiveness of the conditions is demonstrated using several examples. [ABSTRACT FROM AUTHOR]

This technical note addresses the distributed time-varying formation-containment control problem for heterogeneous general linear multiagent systems (the virtual leader, multileaders, and followers) based on the output regulation framework from an observer viewpoint under the directed topology, which contains a spanning tree. All agents can have different dynamics and different state dimensions. A new format of time-varying formation (TVF) shape is proposed. The multileaders are required to achieve the TVF with tracking the virtual leader, whose output is only available to a subset of them, and only need to send the information of their designed observers and TVF shapes to their neighboring followers. A new class of distributed adaptive observer-based controllers is designed with the mild assumption that both leaders and followers are introspective (i.e., agents have knowledge of their own outputs). Compared with the existing works, one main contribution is that the controllers are fully distributed with the proposition of TVF shapes. The simulation to multivehicle systems is also provided to verify the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

Stabilization of linear systems with unknown dynamics is a canonical problem in adaptive control. Since the lack of knowledge of system parameters can cause it to become destabilized, an adaptive stabilization procedure is needed prior to regulation. Therefore, the adaptive stabilization needs to be completed in finite time. In order to achieve this goal, asymptotic approaches are not very helpful. There are only a few existing nonasymptotic results and a full treatment of the problem is not currently available. In this paper, leveraging the novel method of random linear feedbacks, we establish high probability guarantees for finite-time stabilization. Our results hold for remarkably general settings because we carefully choose a minimal set of assumptions. These include stabilizability of the underlying system and restricting the degree of heaviness of the noise distribution. To derive our results, we also introduce a number of new concepts and technical tools to address regularity and instability of the closed-loop matrix. [ABSTRACT FROM AUTHOR]

Opinion dynamics on social networks with coopetitive (cooperative-competitive) interactions may result in polarity, consensus or neutrality under different opinion protocols. The antecedent of protocol design is to study the accessibility problem: whether or not there exist admissible control rules to polarize, consensus, or neutralize individual opinions in a large population. From an operational perspective, this technical note is aimed at the investigation of polarizability, consensusability, and neutralizability of opinion dynamics in question. Particular emphasis is on the joint impact of the dynamical properties of individuals and the interaction topology among them on polarizability, consensusability, and neutralizability, respectively. Sufficient and/or necessary conditions for those accessibility problems are provided by using powerful tools from spectral analysis and algebraic graph theory. To characterize the individual diversity in real life, we further investigate the solvability of opinion formation problems in heterogeneous systems with nonidentical dynamics. Accordingly, sufficient and/or necessary criteria for heterogeneous network polarizability, consensusability, and neutralizability are derived. [ABSTRACT FROM AUTHOR]

High-dimensional systems that have a low-dimensional dominant behavior allow for model reduction and simplified analysis. We use differential analysis to formalize this important concept in a nonlinear setting. We show that dominance can be studied through linear dissipation inequalities and an interconnection theory that closely mimics the classical analysis of stability by means of dissipativity theory. In this approach, stability is seen as the particular situation where the dominant behavior is 0-dimensional. The generalization opens novel tractable avenues to study multistability through 1-dominance and limit cycle oscillations through 2-dominance. [ABSTRACT FROM AUTHOR]

The leader-following consensus problem for linear discrete-time multiagent systems has been studied in the literature using $H_{\infty }$ Riccati inequality design and $H_{2}$ Riccati equation design methods, respectively. These two methods lead to a solvability condition in terms of an inequality that relies on a scaling gain and a fixed weighting vector called nominal weighting vector. In this paper, we further study this problem by proposing a more general class of distributed state feedback control laws, which not only depends on a scaling gain, but also a set of weighting vectors. We first establish a spectral property of a weighted graph matrix, which will be instrumental in solving the problem. Then, we present a solvability condition based on a modified algebraic Riccati equation, which is somehow more general than $H_{\infty }$ and $H_{2}$ Riccati methods, in that the solvability condition can be made satisfied by tuning the weighting vector. We show that our solvability condition is also necessary for single-input follower systems and is always satisfied for leader systems without exponentially growing modes. Moreover, in case the solvability condition is not satisfied under the nominal weighting vector, we show that our solvability condition can always be made satisfied by choosing a weighting vector other than the nominal one for multiagent systems over acyclic digraphs. [ABSTRACT FROM AUTHOR]

This technical note considers a consensus problem of high-order multiagent systems with antagonistic interactions and communication noises. The interaction network associated with the multiagent system is modeled by a signed graph (called coopetition network) and the agent dynamics is described by a general linear system. A novel stochastic-approximation based control strategy is designed for each agent by using the relative state information from its neighbors. Additionally, convergence of a consensus error system is analyzed by the stochastic stability theory. Finally, the effectiveness of our results is demonstrated by simulation. [ABSTRACT FROM AUTHOR]

This paper investigates the regulation problem for nonminimum-phase nonlinear systems via slow integrators and high-gain feedback. The developed methodology involves four steps: in the first step, we design a full-information feedback controller for an auxiliary system, which parallels the stabilization of the original system, as pioneered in. In the second step, we use high-gain feedback to stabilize the original system, which is able to recover the performance of the auxiliary system by choosing the gain high enough. In the third step, with a condition on the dc steady-state input–output map, a slow integrator is added that enforces the objective of regulation. In the last step, we extend the methodology into the output feedback case by utilizing the extended high-gain observer to estimate the derivatives of the output as well as one unknown term including system uncertainties. The use of the observer recovers the performance under full-information feedback. The design procedure is first presented for the linear model for the clarity of the proposed methodology. The effectiveness of such methodology is demonstrated on the nontrivial translational oscillator rotating actuator example. At last, the design for minimum-phase nonlinear systems is also provided. In this case, the performance recovery of the closed-loop auxiliary system by output feedback is verified. [ABSTRACT FROM AUTHOR]

On a widely studied linear time-invariant (LTI) multiagent consensus dynamics with delays, we study how large the delay can be permitted to be before the dynamics becomes unstable. We present an analytical approach to show how this delay bound, namely, the delay margin, is affected with different underlying graphs obtained by edge elimination. [ABSTRACT FROM AUTHOR]

An adaptive distributed observer was recently proposed to solve the cooperative output regulation problem for discrete-time linear multi-agent systems. The validity of this approach relies on the assumptions that all the eigenvalues of the leader's system matrix are inside or on the unit circle and the solution to the regulator equations is unique. Besides, the range of the observer gains of the adaptive distributed observer is determined by the spectrum of a graph matrix of the communication network, which is not desirable in applications. To overcome these drawbacks, in this paper, we will first propose a new type of the discrete-time adaptive distributed observer for the leader system, whose observer gains are fixed and hence are independent of the communication network, and moreover, this observer allows the eigenvalues of the leader's system matrix to be inside a circle with radius strictly greater than one. Then, we will strengthen the existing adaptive control approach so that it can handle the case where the solution to the regulator equations is not unique. These improvements have not only made our approach more practical, but also enlarged the systems that can be handled by the existing approach. [ABSTRACT FROM AUTHOR]

This paper considers the design of observers for systems with slow and fast modes. The existing methods are able to design independent slow and fast observers with $O(\epsilon)$ accuracy only, where $\epsilon$ is a small positive singular perturbation parameter that indicates separation of system state-space variables into slow and fast. In this paper, the design of independent slow and fast reduced-order observers was performed with very high accuracy $O(\epsilon ^{i}), i=2,3,....$. The results obtained are extended to the design of corresponding observer driven controllers. The design allows complete time-scale separation for both the observer and controller through the decomposition into slow and fast time scales. This method reduces both offline and online computations. The effectiveness of the new methods is demonstrated through both theoretical and simulation results. [ABSTRACT FROM AUTHOR]

We consider the problem of distributed state estimation of a linear time-invariant (LTI) system by a network of sensors. We develop a distributed observer that guarantees asymptotic reconstruction of the state for the most general class of LTI systems, sensor network topologies, and sensor measurement structures. Our analysis builds upon the following key observation—a given node can reconstruct a portion of the state solely by using its own measurements and constructing appropriate Luenberger observers; hence, it only needs to exchange information with neighbors (via consensus dynamics) for estimating the portion of the state that is not locally detectable. This intuitive approach leads to a new class of distributed observers with several appealing features. Furthermore, by imposing additional constraints on the system dynamics and network topology, we show that it is possible to construct a simpler version of the proposed distributed observer that achieves the same objective while admitting a fully distributed design phase. Our general framework allows extensions to time-varying networks that result from communication losses, and scenarios including faults or attacks at the nodes. [ABSTRACT FROM AUTHOR]

This paper addresses the cooperative output regulation problem of heterogeneous linear multi-agent systems with directed communication topologies, requiring only intermittent communication. First, we propose a unified framework of time- and event-triggering strategies. Then based on the unified triggering framework, a novel triggering mechanism utilizing the self-triggering strategy is developed. It is shown that with the proposed triggering mechanism, the cooperative output regulation problem can be solved by a distributed control law with only intermittent communication. It is further shown that with the unified framework of time- and event-triggering strategies for each agent, a positive minimum inter-event time can be explicitly given and Zeno behavior can be thus excluded. An example is finally provided to demonstrate the effectiveness of the proposed controller and the triggering mechanism. [ABSTRACT FROM PUBLISHER]

This paper presents theoretical guarantees for the stability and performance for the singular value decomposition (SVD) system. The SVD System uses the SVD to reduce the dimension of the control inputs within a feedback loop. This is used to meet the rank 1 input constraint imposed by the row-column structure. The row-column structure reduces the number of inputs required to control $mn$ subsystems to $m + n$. The SVD System provides scalable performance for systems coupled using the row-column structure. The results of this paper are the first analytical results for the SVD System when applied to linear subsystems of arbitrary order. The conclusion of all of this is that using the SVD System allows you to reduce the number of inputs while maintaining as close to the same performance as possible. [ABSTRACT FROM PUBLISHER]