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This paper regards the coordination of networked systems, studied in the framework of hybrid dynamical systems. We design a coordination scheme which combines the use of ternary controllers with a self-triggered communication policy. The communication policy requires the agents to measure, at each sampling time, the difference between their states and those of their neighbors. The collected information is then used to update the control and determine the following sampling time. We show that the proposed scheme ensures finite-time convergence to a neighborhood of a consensus state: the coordination scheme does not require the agents to share a global clock, but allows them to rely on local clocks. We then study the robustness of the proposed self-triggered coordination system with respect to skews in the agents' local clocks, to delays, and to limited precision in communication. Furthermore, we present two significant variations of our scheme. First, assuming a global clock to be available, we design a time-varying controller which asymptotically drives the system to consensus. The assumption of a global clock is then discussed, and relaxed to a certain extent. Second, we adapt our framework to a communication model in which each agent polls its neighbors separately, instead of polling all of them simultaneously. This communication policy actually leads to a self-triggered “gossip” coordination system. [ABSTRACT FROM PUBLISHER]

This paper considers the stability of a single-input single-output (SISO) system with an input/output (I/O) delay, called SISO delay system hereafter. We first derive an algebraic criterion to solve the complete stability w.r.t. the delay $\tau$. Next, the stability analysis is extended to the case with additional free (plant and/or controller) parameters, denoted by a vector $X$. By adopting a mathematical tool for polynomial algebra, the discrimination system, the complete classification of the critical imaginary roots (CIRs) in the whole $X$ - $\tau$ parameter space may be obtained. Furthermore, with the above results, we present the stability crossing sets (SCSs) in a new form, called the colored SCSs. For each point on the SCS the asymptotic behavior information of the corresponding CIR can be coded by a certain color (red, green, or yellow). Hence, the stability in the $X$ - $\tau$ space can be analyzed easily and intuitively. Moreover, the geometry of the SCSs can be investigated from a new perspective, which will help not only to better understand the stability of the SISO delay system but also to considerably simplify the procedure for generating the colored SCSs. [ABSTRACT FROM AUTHOR]

This paper studies regional boundary stabilization of nonlinear Schrödinger equation with state delay and bounded internal disturbance. The boundary constrained control law is designed by using the backstepping method. Regional input-to-state stability of the perturbed system with time-delay is established by a Lyapunov function and a generalized Halanay's inequality. Estimates on the set of initial conditions are found starting from which the solutions are exponentially attracted to a bounded set. A numerical example demonstrates the efficiency of the results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a delay differential inclusion $\dot{x}(t)\in F(t,x_t)$ , where $x_t$ denotes the history function of $x(\cdot)$ along an interval of time. We extend the celebrated Filippov's theorem to this case. Then, we further generalize this theorem to the case when the state variable $x$ is constrained to the closure of an open subset $K\subset \mathbb {R}^n$. Under a new “inward pointing condition,” we give a relaxation result stating that the set of trajectories lying in the interior of the state constraint is dense in the set of constrained trajectories of the convexified inclusion ${\dot{x}(t)\in \mbox{co}\,F(t,x_t)}$. [ABSTRACT FROM AUTHOR]

Event-triggered control is an effective control strategy, capable of reducing the amount of communications and retaining a satisfactory closed-loop performance. In this paper, we aim at proposing an event-triggered sampling mechanism and studying observer-based output feedback control for switched linear neutral systems with mixed time-varying delays. Different from the conventional event-triggered control strategies, our proposed one transmits not only the state but also the switching information to the controller, which is advantageous in applications where the measured outputs and the switching information have to be transmitted over a communication network. Moreover, asynchronous switchings may be caused between the subsystems and their matched subcontrollers under the proposed sampling mechanism, which increases difficulties in analyzing stability. We develop a sufficient condition, under which the proposed control scheme guarantees globally the exponential stability of the closed-loop system meanwhile taking into account asynchronous switchings. Finally, an illustrative example is given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we prove a theorem of linearized asymptotic stability for nonlinear fractional differential equations with a time delay. By using the method of linearization of a nonlinear equation along an orbit (Lyapunov's first method), we show that an equilibrium of a nonlinear Caputo fractional delay differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. Our approach is based on a technique that converts the linear part of the equation into a diagonal one. Then by using the properties of generalized Mittag-Leffler functions, the construction of an associated Lyapunov–Perron operator, and the Banach contraction mapping theorem, we obtain the desired result. [ABSTRACT FROM AUTHOR]

This paper addresses the boundary stabilization problem of one-dimensional linear parabolic systems with input delay. Especially, the case of Neumann boundary control is studied. The purpose is to derive the stabilizing controller of predictor type in a Hilbert space, by using a backstepping method combined with the semigroup theory. The use of the semigroup theory makes the proof of continuity of the inverse transformation easy. Also, it is shown that the implementation of the abstract controller is feasible by using a finite number of eigenvalues and eigenfunctions of the system operator. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a passivity-based design framework for event-triggered networked control systems. We consider the effects of network-induced time delays, signal quantization, and data loss in communication links between the plant and controller and show $L_2$ -stability and robustness for the control design. We introduce simple asynchronous triggering conditions that do not rely on the exact knowledge of the systems’ dynamics and are located on both sides of the communication network. This leads to a great decrease in the communication rate between systems. Additionally, we show lower bounds on interevent time intervals for the triggering conditions and characterize the design's robustness against external disturbances. We illustrate the relationship among stability, robustness, and passivity levels of the plant and controller. Moreover, we analyze our design's robustness against packet dropouts. Finally, we calculate the passivity levels for the entire event-triggered networked control system. This is beneficial in design of compositional networked control systems. Our results are design-oriented. By following our proposed framework, the designer can characterize clear tradeoffs among passivity levels, design parameters, time delays, effects of signal quantization and triggering conditions, stability, robustness, and performance, and make design decisions accordingly. [ABSTRACT FROM AUTHOR]

This paper studies the linear–quadratic mean-field game (MFG) for a class of stochastic delayed systems. We consider a large-population system, where the dynamics of each agent is modeled by a stochastic differential delayed equation. The consistency condition is derived through an auxiliary system, which is an anticipated forward–backward stochastic differential equation with delay (AFBSDDE). The wellposedness of such an AFBSDDE system can be obtained using a continuation method. Thus, the MFG strategies can be defined on an arbitrary time horizon, not necessary on a small time horizon by a commonly used contraction mapping method. Moreover, the decentralized strategies are verified to satisfy the $\epsilon$ -Nash equilibrium property. For illustration, three special cases of delayed systems are further explored, for which the closed-loop and open-loop MFG strategies are derived, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we present Lyapunov characterizations of the global asymptotic stability, the input-to-state stability (ISS), and the incremental input-to-state stability ($\delta$ -ISS) for discrete-time nonlinear systems with uncertain and time-varying time delays. We provide necessary and sufficient conditions for the global asymptotic stability and for the ISS and sufficient conditions for the $\delta$-ISS, in terms of discrete-time Lyapunov–Krasovskii functionals. In particular, the Lyapunov characterization of the notion of $\delta$-ISS is motivated by problems concerning the construction of discrete abstractions approximating discrete-time nonlinear systems. Uncertain and time-varying time delays occur very frequently, for instance, in networked control systems. Examples are included that illustrate the proposed methodologies. [ABSTRACT FROM AUTHOR]

This paper studies the problem of global state regulation with stability for time-delay nonlinear systems with unknown control directions. Using a dynamic gain-based method for counteracting time-delay nonlinearity and the Nussbaum-gain function for dealing with unknown control directions, we develop a dynamic state feedback control strategy that solves the problem. A novel construction of Lyapunov–Krasovskii functionals is presented and plays a key role in handling nonlinearity with delayed states and unknown control directions simultaneously. The proposed dynamic state feedback compensators are shown to guarantee 1) global asymptotic convergence of the system state to the origin and 2) global boundedness of the resulting closed-loop systems. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability analysis for continuous-time positive singular systems with time-varying delays. First, an auxiliary system is introduced to establish the positivity condition for singular time-delay systems. Based on the positivity condition, the stability criterion is obtained for the positive singular systems with constant delays. By analyzing the monotonic property of the system trajectory, we extend the stability condition to the cases with time-varying delays. A numerical simulation is employed to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper is devoted to a distributed consensus problem for second-order multiagent systems with nonconvex velocity and control input constraints. A distributed control algorithm is introduced using local information. It is shown that consensus can be achieved as long as the union of the communication graphs has directed spanning trees among each time interval of certain bounded length in the presence of arbitrarily bounded communication delays. Finally, a numerical example is included to illustrate the theoretical results. [ABSTRACT FROM PUBLISHER]

In this paper, we deal with the control of a transport partial differential equation/ nonlinear ordinary differential equation (PDE/nonlinear ODE) cascade system in which the transport coefficient depends on the ODE state. We develop a PDE-based predictor-feedback boundary control law, which compensates the transport dynamics of the actuator and guarantees global asymptotic stability of the closed-loop system. The stability proof is based on an infinite-dimensional backstepping transformation and a Lyapunov-like argument. The relation of the PDE–ODE cascade with a state-dependent propagation speed to an ODE system with a state-dependent input delay, which is defined implicitly via an integral of past values of the ODE state, is also highlighted and the corresponding equivalent predictor-feedback design is presented together with an alternative proof of global asymptotic stability of the closed-loop system based on the construction of a Lyapunov functional. The practical relevance of our control framework is illustrated in an example that is concerned with the control of a metal rolling process. [ABSTRACT FROM PUBLISHER]

In this paper, we extend detectability to delayed detectability in order to answer the following question. After observing k1+k2 observable events, can we determine the state of a system at the time when the k1th event was observed? If the answer is yes, we say that the system is delayed detectable. It involves two delays: the prior delay k1 before the estimation is attempted and the post delay k2 after which the estimation is completed. We investigate various properties of delayed detectability. We also provide polynomial algorithms to check delayed detectability. The usefulness of delayed detectability is not only evident by the state estimation problems it solves, which include current state estimation problem and initial state estimation problem, but also evident by the fact that two important properties in discrete event systems, namely observability and diagnosability, can both be shown to be special cases of delayed detectability. [ABSTRACT FROM AUTHOR]

There are many communication imperfections in networked control systems (NCS) such as varying transmission delays, varying sampling/transmission intervals, packet loss, communication constraints and quantization effects. Most of the available literature on NCS focuses on only some of these aspects, while ignoring the others. In this paper we present a general framework that incorporates communication constraints, varying transmission intervals and varying delays. Based on a newly developed NCS model including all these network phenomena, we will provide an explicit construction of a continuum of Lyapunov functions. Based on this continuum of Lyapunov functions we will derive bounds on the maximally allowable transmission interval (MATI) and the maximally allowable delay (MAD) that guarantee stability of the NCS in the presence of communication constraints. The developed theory includes recently improved results for delay-free NCS as a special case. After considering stability, we also study semi-global practical stability (under weaker conditions) and performance of the NCS in terms of Ꮭp gains from disturbance inputs to controlled outputs. The developed results lead to tradeoff curves between MATI, MAD and performance gains that depend on the used protocol. These tradeoff curves provide quantitative information that supports the network designer when selecting appropriate networks and protocols guaranteeing stability and a desirable level of performance, while being robust to specified variations in delays and transmission intervals. The complete design procedure will be illustrated using a benchmark example. [ABSTRACT FROM AUTHOR]

This paper considers synchronous and asynchronous heterogeneous cyclic pursuit in discrete time and obtains results on the consensus of both. It is shown that agents in synchronous heterogeneous cyclic pursuit system can achieve consensus with at most one negative gain, subject to a lower limit, which expands the reachable set although the asynchronous case may diverge when one of the agents has a negative gain. However, when all the gains are positive, positional consensus is achieved even in the asynchronous mode. The theoretical results are illustrated through simulations. [ABSTRACT FROM AUTHOR]

The problem of state estimation for nonlinear systems with unknown state or measurement delays is still an open problem. In this paper, we consider the case of measurement delay and propose an approach that combines a delay identifier with a suitable high-gain observer in order to achieve simultaneous estimation of state and delay. We provide sufficient conditions that guarantee the exponential convergence to zero of the errors, globally with respect to the system variables and locally with respect to the delay estimation. We validate the method through an example concerning population models. [ABSTRACT FROM AUTHOR]

This paper considers the eigenvalue distribution of a linear time-invariant (LTI) system with commensurate time delays and its application to proportional-integral-derivative (PID) controller design for a delay plant via dominant eigenvalue assignment. A new result on the root distribution of a quasi-polynomial is first produced by applying part of Pontryagin's conclusions. This result which gives a necessary and sufficient condition can be directly used to judge the number of the right-half plane eigenvalues of the characteristic equation of a time delay system. Based on the proposed result, necessary and sufficient conditions on dominant eigenvalue assignment for PID control of time delay systems are presented and an algorithm is then provided to determine the PID controller gains. The proposed approaches can assign some (one or two) eigenvalues to the desired positions and all the other eigenvalues to the left of a given line to guarantee the dominance of the assigned ones, which enables us to design the controller according to the desired performance indexes for a standard first-order system or a standard second-order system in addition to stability. The method is effective for the closed-loop characteristic equation being retarded type or neutral type. The controller gains to achieve the control objective can be characterized by a straightforward computation. Further, a result on degradation to proportional-integral (PI) control of time delay systems is given. [ABSTRACT FROM AUTHOR]

We have previously introduced an inference-based framework for decentralized decision-making, comprising of multiple observers, each with its own partial observation, where inferencing over the ambiguities of the self and the others is used to issue local decisions, and a global decision is taken to be the one possessing the minimum ambiguity level. In this setting, we previously introduced the notion of $N$ -inference $\vee$ -diagnosability to characterize the existence of a disjunctive decentralized diagnosis scheme so that any fault can be detected within a bounded delay, using at most $N$ -levels of inferencing, by one of the diagnosers. While the disjunctive scheme relies on one of the diagnosers making the failure decision, the dual conjunctive scheme relies on none of the diagnosers making the nonfailure decision. It is known that the two schemes are incomparable, and in this paper we extend our earlier work to provide a more general framework, introducing the notion of $N$ -inference diagnosability, capturing both disjunctive and conjunctive schemes. We also develop a method for verifying $N$-inference diagnosability, as well as discuss several of its useful properties. [ABSTRACT FROM AUTHOR]

The quickest change detection problem is to detect an abrupt change event as quickly as possible subject to constraints on false detection. Unlike the classical problem, where the decision maker can access only one sequence of observations, in this paper, the decision maker chooses one of two different sequences of observations at each time instant. The information quality and sampling cost of the two sequences of observations are different. We present an asymptotically optimal joint design of observation scheduling policy and stopping time such that the detection delay is minimized subject to constraints on both average run length to false alarm (ARLFA) and average cost per sample. The observation scheduling policy has a threshold structure and the detection scheme is a variant of the cumulative sum test where the detection statistic stochastically crosses the threshold that is used to switch observation modes. We further study the decentralized case in a multi-channel setting. We show that if each sensor uses the proposed observation scheduling policy locally and the fusion center uses the N\mathrm{sum} algorithm, by which the center declares the change when the sum of the sensors' local detection statistics crosses a certain threshold, the detection delay is asymptotically minimized for any possible combination of the affected sensors subject to constraints on both global ARLFA and average cost per sample at each sensor node. Numerical examples are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

This paper addresses the leader-follower synchronization problem of uncertain networked Euler-Lagrange systems under directed interconnection graphs in the presence of communication constraints. We present an adaptive distributed control algorithm such that a group of Euler-Lagrange systems asymptotically synchronize their states to those of a dynamic leader with a time-varying trajectory. The information exchange between all systems in the network is assumed to be discrete in time, intermittent, and subject to irregular communication delays and possible packets dropouts. It is shown that leader-follower synchronization is reached for arbitrary characteristics of the communication process provided that the directed interconnection graph contains a spanning tree. Simulation results are given to illustrate the effectiveness of the proposed control scheme. [ABSTRACT FROM PUBLISHER]

A new stabilization approach for linear plants with input delay and an unknown harmonic disturbance affecting the input and the output is presented. To solve this problem, the well-known predictor feedback approach with a state observer and an adaptive scheme, identifying the frequency of the disturbance, is combined. Compared to the existing approaches, the structure of our adaptive scheme is simpler. The proposed approach is applicable to plants of arbitrary relative degree, that may be unstable and non-minimum phase. [ABSTRACT FROM AUTHOR]

This paper is concerned with the long-standing problems of linear quadratic regulation (LQR) control and stabilization for a class of discrete-time stochastic systems involving multiplicative noises and input delay. These fundamental problems have attracted resurgent interests due to development of networked control systems. An explicit analytical expression is given for the optimal LQR controller. More specifically, the optimal LQR controller is shown to be a linear function of the conditional expectation of the state, with the feedback gain based on a Riccati-ZXL difference equation. It is also shown that the system is stabilizable in the mean-square sense if and only if an algebraic Riccati-ZXL equation has a particular solution. These results are based on a new technical tool, which establishes a non-homogeneous relationship between the state and the costate of this class of systems, and the introduction of a new Lyapunov function for the finite-horizon optimal control design. [ABSTRACT FROM PUBLISHER]

This paper proposes an online approach for fault diagnosis of timed discrete event systems modeled by Time Petri Net (TPN). The set of transitions is partitioned into two subsets containing observable and unobservable transitions, respectively. Faults correspond to a subset of unobservable transitions. In accordance with most of the literature on discrete event systems, we define three diagnosis states, namely normal, faulty and uncertain states, respectively. The proposed approach uses a fault diagnosis graph, which is incrementally computed using the state class graph of the unobservable TPN. After each observation, if the part of FDG necessary to compute the diagnosis states is not available, the state class graph of the unobservable TPN is computed starting from the consistent states. This graph is then optimized and added to the partial FDG keeping only the necessary information for computation of the diagnosis states. We provide algorithms to compute the FDG and the diagnosis states. The method is implemented as a software package and simulation results are included. [ABSTRACT FROM AUTHOR]

We investigate supervisory control of networked discrete event systems with asynchronous communication between the plant and supervisor. The observation and control may be randomly delayed. The delays are bounded and will not change the order of observation (FIFO). Our goal is to synthesize a supervisor such that the behavior of the supervised system is both adequate and legal (safe). We derive a necessary and sufficient condition for the existence of such a supervisor. When the condition is satisfied, we find a minimally-permissive state-estimate-based control policy which can be implemented offline or online. Furthermore, we derive an algorithm to check the condition for the existence of the supervisor by constructing an augmented automaton. The algorithm allows us to obtain a maximally-permissive control policy by iteration. [ABSTRACT FROM PUBLISHER]

We present a new approach for the stability analysis of linear coupled differential-difference systems with a general distributed delay. The distributed delay term in this note can contain any ${\mathbb{L}}^{2}$ function which is approximated via a class of elementary functions including polynomial, trigonometric, exponential functions, etc. Through the application of a new proposed integral inequality, a sufficient condition for the stability of the system is derived in terms of linear matrix inequalities based on the construction of a Lyapunov Krasovskii functional. The methods proposed in this note can handle problems that cannot be dealt using existing approaches. Two numerical examples are presented to show the effectiveness of our proposed stability condition. [ABSTRACT FROM AUTHOR]

The agents’ deployment over a line segment under protocols with communication delays and switching is studied. It is assumed that no information about the value of the communication delay and no information about switching policy in the communication graph is available. It is shown that neither delay values nor switching policy in a natural class may influence convergence of the agent states to the equidistant distribution over the line segment. Similar result is obtained for deployment over the circle. The theoretical results are illustrated by simulations. The proofs relay on both well-known and recent approaches to the stability analysis of positive systems. [ABSTRACT FROM AUTHOR]

We present a dual form of Lyapunov–Krasovskii functional which allows the problem of controller synthesis for multidelay systems to be formulated and solved in a convex manner. First, we give a generalized version of the dual stability condition formulated in terms of Lyapunov operators which are positive, self-adjoint, and preserve the structure of the state space. Second, we provide a class of such operators and express the stability conditions as positivity and negativity of quadratic Lyapunov–Krasovskii functional forms. Next, we adapt the Sum of Squares (SOS) methodology to express positivity and negativity of these forms as Linear Matrix Inequalities (LMIs), describing a new set of polynomial manipulation tools designed for this purpose. We apply the resulting LMIs to a battery of numerical examples and demonstrate that the stability conditions are not significantly conservative. Finally, we formulate a test for controller synthesis for systems with multiple delays, apply the test to a numerical example, and simulate the resulting closed-loop system. [ABSTRACT FROM AUTHOR]

We consider the problem of multiagent consensus where some agents are subject to faults/attacks and might make updates arbitrarily. The network consists of agents taking integer-valued (i.e., quantized) states under directed communication links. The goal of the healthy normal agents is to form consensus in their state values, which may be disturbed by the non-normal, malicious agents. We develop update schemes to be equipped by the normal agents whose interactions are asynchronous and subject to nonuniform and time-varying time delays. In particular, we employ a variant of the so-called mean subsequence reduced algorithms, which have been long studied in computer science, where each normal agent ignores extreme values from its neighbors. We solve the resilient quantized consensus problems in the presence of totally/locally bounded adversarial agents and provide necessary and sufficient conditions in terms of the connectivity notion of graph robustness. Furthermore, it will be shown that randomization is essential both in quantization and in the updating times when normal agents interact in an asynchronous manner. The results are examined through a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, we address the design and analysis of multi-variable extremum seeking for static maps subject to arbitrarily long time delays. Both Gradient and Newton-based methods are considered. Multi-input systems with different time delays in each individual input channel as well as output delays are dealt with. The phase compensation of the dither signals and the inclusion of predictor feedback with a perturbation-based (averaging-based) estimate of the Hessian allow to obtain local exponential convergence results to a small neighborhood of the optimal point, even in the presence of delays. The stability analysis is carried out using backstepping transformation and averaging in infinite dimensions, capturing the infinite-dimensional state due the time delay. In particular, a new backstepping-like transformation is introduced to design the predictor for the Gradient-based extremum seeking scheme with multiple and distinct input delays. The proposed Newton-based extremum seeking approach removes the dependence of the convergence rate on the unknown Hessian of the nonlinear map to be optimized, being user-assignable as in the literature free of delays. A source seeking example illustrates the performance of the proposed delay-compensated extremum seeking schemes. [ABSTRACT FROM PUBLISHER]

The theory of pulse-coupled oscillators provides a framework to formulate and develop self-organizing synchronization strategies for wireless communications and mobile computing. These strategies show low complexity and are adaptive to changes in the network. Even though several protocols have been proposed and theoretical insight was gained there is no proof that guarantees synchronization of the oscillator phases in general dynamic coupling topologies under technological constraints. Here, we introduce a family of coupling strategies for pulse-coupled oscillators and prove that synchronization emerges for systems with arbitrary connected and dynamic topologies, individually changing signal propagation and processing delays, and stochastic pulse emission. It is shown by simulations how unreliable links or intentionally incomplete communication between oscillators can improve synchronization performance. [ABSTRACT FROM AUTHOR]

This paper utilizes the concept of a transport partial differential equation (PDE) representation of delayed input to solve the classic problem of output feedback control for a common category of uncertain minimum phase linear time-delay systems in spite of co-existence of unknown plant parameter and actuator delay, as well as unmeasurable ordinary differential equation (ODE) and PDE state. In the case of measurable distributed input, the time-varying trajectory tracking is established while in the other case of unmeasurable distributed input, the constant set-point regulation is accomplished. The applicable output feedback control design incorporates the adaptive backstepping technique for ODE plants with the prediction-based boundary control method for PDE systems. There is not any limitation on relative degree of the considered systems. The Lyapunov-based analysis shows the local stability of the closed-loop ODE-PDE cascade systems. [ABSTRACT FROM PUBLISHER]

The problem of H\infty state-feedback control of linear continuous-time systems with state multiplicative noise in the presence of input delay is investigated. A predictor-based control is applied, for the first time, to these systems. A new condition for stability is derived in a form of a linear matrix inequality. The latter condition is extended to one that guarantees a prescribed \mathcalL2-gain bound for the stochastic system. Solutions are obtained for both constant and time-varying delays. Because of the multiplicative noise, the predictor-based control cannot stabilize the system for arbitrarily large delay. It admits, however, delays that are significantly larger than the delays that can be treated by the corresponding non-predictive state-feedback control. The theoretical results are demonstrated by two examples. The first example shows the advantage of the predictor-based controller and the second one demonstrates the applicability of the theory to process control systems. [ABSTRACT FROM PUBLISHER]

A timed discrete event system, which repeats identical work cycles, has task delays due to synchronization between work cycles. Real such systems tend to operate mostly in a $K$- cyclic timing regime, where a sequence of identical timing patterns is repeated for every $K$ cycles. Therefore, the task delays fluctuate and repeat a sequence of $K$ different values, and hence have higher risk of violating an upper limit. Task delays correspond to token delays at the system's timed event graph model. We therefore examine token delays in $K$- cyclic schedules of a timed event graph, an essential class of Petri nets. We first identify all possible $K$- cyclic schedules and define their initial phases. We then develop a closed-formula on the token delays on a path for a $K$- cyclic schedule, which can be computed by the longest path lengths between the nodes in an associated directed graph. We also present a formula for 1-cyclic schedules. The formulae can be used for computing statistics on $K$- different token delays, maximizing or minimizing the token delays with regard to all possible initial phases, and verifying task delay constraints, if any. [ABSTRACT FROM PUBLISHER]

Networked systems present some key new challenges in the development of fault-diagnosis architectures. This paper proposes a novel distributed networked fault detection methodology for large-scale interconnected systems. The proposed formulation incorporates a synchronization methodology with a filtering approach in order to reduce the effect of measurement noise and time delays on the fault detection performance. The proposed approach allows the monitoring of multirate systems, where asynchronous and delayed measurements are available. This is achieved through the development of a virtual sensor scheme with a model-based resynchronization algorithm and a delay compensation strategy for distributed fault-diagnostic units. The monitoring architecture exploits an adaptive approximator with learning capabilities for handling uncertainties in the interconnection dynamics. A consensus-based estimator with time-varying weights is introduced, for improving fault detectability in the case of variables shared among more than one subsystem. Furthermore, time-varying threshold functions are designed to prevent false-positive alarms. Analytical fault detectability sufficient conditions are derived, and extensive simulation results are presented to illustrate the effectiveness of the distributed fault detection technique. [ABSTRACT FROM PUBLISHER]

The traditional Bayesian approximation framework for filtering in discrete time systems assumes that the measurement is available at every time instant. But in practice, the measurements could be randomly delayed. In the literature, the problem has been examined and solution is provided by restricting the maximum number of delay to one or two time steps. This technical note develops an approach to deal with the filtering problems with an arbitrary number of delays in measurement. Pursuing this objective, traditional Bayesian approximation to nonlinear filtering problem is modified by reformulating the expressions of mean and covariances which appear during the measurement update. We use the cubature quadrature rule to evaluate the multivariate integral expressions for the mean vector and the covariance matrix which appear in the developed filtering algorithm. We compare the new algorithm which accounts for delay with the existing CQKF heuristics on two different examples and demonstrate how accounting for a random delay improves the filtering performance. [ABSTRACT FROM PUBLISHER]

This technical note addresses stability problems of delay differential inclusions. A chain rule is proposed for a wide class of Lyapunov-Krasovskii functionals which are not necessarily invariantly differentiable. We also obtain an invariance-like theorem, where the derivative of the candidate functional is bounded above by a continuous negative semidefinite function. Several examples are given to show the effectiveness of the results. [ABSTRACT FROM AUTHOR]

We study the stability of networks of multi-agent systems with local pinning strategies and two types of time delays, namely the transmission delay in the network and the pinning delay of the controllers. Sufficient conditions for stability are derived under specific scenarios by computing or estimating the dominant eigenvalue of the characteristic equation. In addition, controlling the network by pinning a single node is studied. Moreover, perturbation methods are employed to derive conditions in the limit of small and large pinning strengths. Numerical algorithms are proposed to verify stability, and simulation examples are presented to confirm the efficiency of analytic results. [ABSTRACT FROM AUTHOR]

Necessary stability conditions for linear systems with multiple pointwise and distributed delays are presented. New properties that connect the Lyapunov delay matrix and the fundamental matrix of these systems are instrumental in proving that these conditions depend exclusively on the Lyapunov delay matrix. The result is illustrated by some examples. [ABSTRACT FROM PUBLISHER]

Global delay independent stability is analyzed for nonlinear time-delay systems by applying homogeneity theory. It is shown that finite-time stability can be encountered in this class of systems under uniformity of the convergence time with respect to delay. Some additional tools for stability analysis of time-delay systems using homogeneity are also presented: in particular, it is shown that if a time-delay system is homogeneous with nonzero degree and it is globally asymptotically stable for some delay, then this property is preserved for any delay value, which is known as the independent of delay stability. [ABSTRACT FROM AUTHOR]

This technical note addresses the stability analysis of linear systems governed by continuous-time difference equations with multiple delays. We propose new sufficient conditions for L2-exponential stability and exponential stability within the Lyapunov-Krasovskii framework. These conditions are delay-independent, and provide constructive exponential decay rate estimates of the system response. It is also shown that these conditions are less conservative than previous results in the literature. [ABSTRACT FROM AUTHOR]

The Universal Integral Control, introduced by H.K. Khalil (Universal integral controllers for minimum-phase nonlinear systems, IEEE Trans. Autom. Control, vol. 45, no. 3), is revisited by employing mollifiers instead of a high-gain observer for the differentiation of the output signal. The closed-loop system is a classical functional differential equation with distributed delays on which standard Lyapunov arguments are applied to study the stability. Low-pass filtering capability of mollifiers is demonstrated for a high amplitude and rapidly oscillating noise. The controller is supported by numerical simulations. [ABSTRACT FROM AUTHOR]

Motivated by control applications relying on shared resources (such as computation time or bandwidth), we analyze the stability and robustness of discrete-time switched linear systems with stochastic commutations. We show that a wide class of shared resources control strategies can be modeled by a stochastic jump linear system involving two stochastic processes. The class of systems we study encompasses Markov chains and independent and identically distributed switching processes. For these systems, we recall existing definitions of stability and robustness, by relying on the input-to-state stability (ISS) property. We show that, for the class of systems under concern, $\delta$-moment stability is equivalent to $\delta$-moment ISS and that they both imply almost sure ISS. Several sufficient conditions are provided to guarantee these properties. Anytime control design for a translational oscillator/rotational actuator (TORA) system is used to illustrate all these concepts. [ABSTRACT FROM PUBLISHER]

This article investigates the robust cooperative output regulation problem of heterogeneous uncertain linear multiagent systems with switching topologies and infinite distributed communication delays. A novel distributed observer is proposed for each agent to estimate the state of the so-called exosystem by taking consideration of both switching topologies and infinite distributed communication delays. A distributed output feedback controller is then developed based on the internal model principle and the estimated state without using the prior knowledge of communication delays. It is shown via the newly developed Lyapunov-like method that the robust cooperative output regulation problem can be solved under some mild assumptions. Finally, a numerical example is given to demonstrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

This article considers the distributed resource allocation problem over a network of n agents with individual optimization functions and coupled resource constraints. The optimization variables are bounded for each agent. We propose an asynchronous distributed gradient descent based method, which is able to tackle time-varying communication networks and communication problems. The main ideas are twofold. First, the degree of freedom of the network is reduced to deal with the global constraint. Second, we utilize delay compensation to counteract the delay of asynchronous communication. We prove that the convergence rate is $O(\frac{1}{k})$ and analyze both the communication complexity and the time complexity. This method is applied into the parallel pump control problem in HVAC system and shows good numerical results. [ABSTRACT FROM AUTHOR]

This article investigates the problem of how to control nonlinear systems with delays in the state by memoryless linear feedback. The notions of semiglobal asymptotic stabilization and sublevel sets are introduced in the context of time-delay systems. With the aid of Razumikhin theorem, we develop a semiglobal design method for the construction of Lyapunov functions, associated sublevel sets, and delay-free linear state feedback laws, step-by-step, achieving semiglobal asymptotic stabilization for time-delay nonlinear systems in a lower triangular form. In contrast to the global stabilization of nonlinear systems with delays in the state, which is usually achieved by dynamic state feedback (Lin and Zhang, 2020), the significance of this work is to point out that a tradeoff of the control objectives, e.g., semiglobal versus global stabilization, makes it possible to control a class of time-delay nonlinear systems by static linear feedback. Extensions to nonlinear systems with globally asymptotically locally expoentially stable (GALES)-like inverse dynamics are also included in this article. [ABSTRACT FROM AUTHOR]

For a family of genuinely nonlinear systems with delays in the input and state, global strong stabilization (GSS) in the sense of Kurzweil is shown to be possible by memoryless state and/or output feedback under two conditions: 1) The input delay is within an appropriate range although the state delays can be sufficiently large; 2) the time-delay bounding system is homogeneous of degree zero and has a lower triangular structure. The proof is based on the Lyapunov–Krasovskii functional theorem combined with the homogeneous domination philosophy. Using the emulation approach, we design memoryless homogeneous state and output feedback controllers, respectively, achieving GSS of the time-delay closed-loop systems with severe nonlinearity. Extensions to a wider class of time-delay nonlinear systems in the Hessenberg form are also given. Examples and counter-examples presented in this article illustrate not only the necessity of the homogeneous growth conditions but also the significance of the memoryless non-Lipschitz continuous feedback control strategies. [ABSTRACT FROM AUTHOR]