Event-Triggered Stabilization of a Linear System With Model Uncertainty and i.i.d. Feedback Dropouts.

We develop tools for investigation of input-to-state stability (ISS) of infinite-dimensional control systems. We show that for certain classes of admissible inputs the existence of an ISS-Lyapunov function implies the input-to-state stability of a system. Then for the case of systems described by abstract equations in Banach spaces we develop two methods of construction of local and global ISS-Lyapunov functions. We prove a linearization principle that allows a construction of a local ISS-Lyapunov function for a system which linear approximation is ISS. In order to study interconnections of nonlinear infinite-dimensional systems, we generalize the small-gain theorem to the case of infinite-dimensional systems and provide a way to construct an ISS-Lyapunov function for an entire interconnection, if ISS-Lyapunov functions for subsystems are known and the small-gain condition is satisfied. We illustrate the theory on examples of linear and semilinear reaction-diffusion equations.

In this paper, input-to-state stability (ISS) of continuous-time systems is analyzed via finite-time Lyapunov functions. ISS of a continuous-time system is first proved via finite-time robust Lyapunov functions for an introduced auxiliary system of the considered system. It is then obtained that the existence of a finite-time ISS Lyapunov function implies that the continuous-time system is ISS. The converse finite-time ISS Lyapunov theorem is proposed. Furthermore, we explore the properties of finite-time ISS Lyapunov functions for the continuous-time system on a bounded and compact set without a small neighborhood of the origin. The effectiveness of our results is illustrated by four examples.

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 (δ-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 δ-ISS, in terms of discrete-time Lyapunov-Krasovskii functionals. In particular, the Lyapunov characterization of the notion of δ-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.

This technical note is mainly concerned with bit rate conditions to stabilize a continuous-time scalar linear control system which transmits its feedback information through digital communication networks. It shows that when a packet is received, not only the bits inside that packet but also the receiving time instant of that packet carry information. The latter could carry a huge amount of information and can be obtained through simply receiving a packet without additional communication cost. Therefore it is an efficient way to encode information into the receiving time instant of a packet. The receiving time instant, however, cannot be accurately controlled by the sensor/sampler which can determine only sampling time instants. The difference between the sampling and receiving time instants of a packet is up to two delays, including the delay to process and encode the packet and the network delay to transmit that packet. These delays cannot be precisely known and have negative effects on the amount of information carried by receiving time instants. Under the boundedness assumption of these delays, this technical note provides some bit rate conditions to guarantee the system's input-to-state stability by making a good use of receiving time instants. Through event-triggering schemes, we realize these conditions which may require much lower stabilizing bit rates than periodic sampling schemes. Simulations are done to confirm the effectiveness of the obtained stabilizing bit rate conditions.

This paper studies the problem of event-triggered fault detection filter (FDF) and controller coordinated design for a continuous-time networked control system (NCS) with biased sensor faults. By considering sensor-to-FDF network-induced delays and packet dropouts, which do not impose a constraint on the event-triggering mechanism, and proposing the simultaneous network bandwidth utilization ratio and fault occurrence probability-based event-triggering mechanism, a new closed-loop model for the considered NCS is established. Based on the established model, the event-triggered H ∞ performance analysis, and FDF and controller coordinated design are presented. The combined mutually exclusive distribution and Wirtinger-based integral inequality approach is proposed for the first time to deal with integral inequalities for products of vectors. This approach is proved to be less conservative than the existing Wirtinger-based integral inequality approach. The designed FDF and controller can guarantee the sensitivity of the residual signal to faults and the robustness of the NCS to external disturbances. The simulation results verify the effectiveness of the proposed event-triggering mechanism, and the FDF and controller coordinated design.

This paper introduces appropriate concepts of input-to state stability (ISS) for nonlinear impulsive hybrid systems(NIHS). First we study the case in which one kind of dynamics system without external inputs has a stability property, then by applying the ISS-Lyapunov function theory, several sufficient conditions are derived for the ISS property of the whole NIHS with inputs. The results of ISS are used to study the robustly globally uniformly exponential stability for impulsive hybrid systems. The impulsive hybrid system can keep ISS no matter how often the impulses occur. Our proposed results are evaluated using illustrative example to show their effectiveness.

Recent technological advances have enabled distributed control systems to be implemented via networks. This allows feedback control loops to be closed over a shared communication channel. Network-induced delays are inevitable, however, when transmitting digital data between control devices. This paper analyzes the stability of such networked control systems (NCS). We first review some previous work on this topic, offering some improvements. We analyze the influence of the sampling rate and network delay on system stability. We further study the stability of NCS using a hybrid system stability analysis technique.

This paper overviews the research investigations pertaining to stability and stabilization of control systems with time‐delays. The prime focus is the fundamental results and recent progress in theory and applications. The overview sheds light on the contemporary development on the linear matrix inequality (LMI) techniques in deriving both delay‐independent and delay‐dependent stability results for time‐delay systems. Particular emphases will be placed on issues concerned with the conservatism and the computational complexity of the results. Key technical bounding lemmas and slack variable introduction approaches will be presented. The results will be compared and connections of certain delay‐dependent stability results are also discussed.

Input-to-state stability for networked control system with predictive scheme

Lyapunov characterization of input-to-state stability for semilinear control systems over Banach spaces

This correspondence deals with the problems of analysis and design for a class of continuous-time Takagi-Sugeno fuzzy control systems. Sufficient conditions for the stability of fuzzy control systems are derived based on a fuzzy Lyapunov function. Both parallel and nonparallel distributed compensation controllers are considered. Sufficient conditions for the solvability of the controller design problem are given in the form of linear matrix inequalities. Unlike the fuzzy Lyapunov function approaches reported in the literature, the bound of the time derivatives of the fuzzy basis functions is not required in the proposed approaches. The effectiveness of the proposed approaches is shown through a numerical example.

The structured singular value method is applied to continuous-time SISO repetitive control systems in order to determine their stability and performance robustness in the presence of structured parametric modeling error in the plant. Performance measures for repetitive control systems are introduced and the robust performance analysis using structured singular values is modified, taking the alternating magnitude behaviour of the sensitivity function of a repetitive control system into account. The analysis procedure is simplified considerably in the case of large time delay by noting that the upper and lower envelopes of the structured singular value plots are obtained from corresponding finite dimensional systems without any time delay. The analysis procedures developed are applied to an example on repetitive control of an electrohydraulic material testing machine, available in the literature, to demonstrate their usefulness.

This paper studies the input-to-state stability (ISS) of nonlinear systems in Takagi-Sugeno's form. Following the definitions and ISS properties proposed by Sontag and Wang [1], a condition in terms of Linear Matrix Inequalities (LMIs) and predefined norm-bounded inputs is derived. Due to the convex property of the weighted sum of input matrices, the input field is bounded and the ISS property holds for systems that are global asymptotic stable (GAS) in the absence of exogenous inputs. First, a existing ISS condition for Takagi-Sugeno (TS) systems that fulfill standard quadratic Lyapunov function is revisited. Then, a ISS condition using a non-quadratic Lyapunov function candidate is derived. To illustrate the applicability of both conditions two numerical examples are studied.

This article addresses a class of large-scale stochastic impulsive systems with time delay and time-varying input disturbance having bounded magnitude. The main interest is to develop sufficient conditions for the input-to-state stability (ISS) and stabilization in the presence of impulsive effects. The method of Razumikhin–Lyapunov function is used to develop the ISS and stabilization properties. Later, these results are applied to a class of control systems where the controller actuators are susceptible to failures. It should be noted that our results are delay independent, and the designed reliable controller is robust with respect to the actuator failures and to the system uncertainties. It is also observed that if the isolated continuous system is ISS and subjected to bounded impulsive effects, then the resulting impulsive system preserves the ISS property. Moreover, if the isolated continuous subsystems are all ISS and the interconnection amongst them is bounded from above, then the impulsive interconnected system is ISS provided that the degree of stability of each subsystem is larger than the magnitude of interconnection. If the underlying continuous system is unstable, then the input-to-state stabilization of the impulsive system is guaranteed if the stabilizing impulses are applied to the system frequently. As an implication to these results, if the input disturbance is zero, then the input-to-state stability (or stabilization) reduces to the stability (or stabilization) of the equilibrium state of the underlying disturbance-free system. A numerical example and simulations are provided to illustrate the proposed results.

This paper continues with the development of the input‐to‐state stability (ISS)‐control Leonov function (CLeF) approach. The definitions of practical ISS and integral ISS (iISS)–CLeFs are refined, and the proposed methodology for control synthesis is improved to simplify the final control law. Then, it is shown that the existence of practical ISS‐ and iISS–CLeFs is a sufficient condition to guarantee the existence of a controller that endows multistable state periodic systems with the ISS and iISS properties, respectively. Furthermore, a methodology for the design of such a controller is provided via the well‐known Sontag's universal formula. Besides, an extension of the main result is presented to connect the ISS–CLeF approach with the standard Leonov function method such that the maximal invariant set of the closed‐loop system is compact on a manifold. Finally, the proposed approach is applied to the design of an excitation controller for a synchronous generator, which guarantees global ISS properties for the closed‐loop system, unlike the usual local results reported in the literature. The obtained control is also independent of the load angle. The effectiveness of the designed controller is demonstrated in simulations.