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In this chapter, we study the observer-based output feedback control problem for a class of switched linear neutral systems under an event-triggered sampling mechanism and for the first time address event-triggered control of switched linear neutral systems. Switched neutral systems are a special kind of switched delay systems but with more complexity structure in which at least one subsystem is a neutral system.

In this chapter, we study the problem of robust fault-tolerant control of a class of switched cascade nonlinear systems with structural uncertainties existing in both system matrices and input matrices, and proposes a fault-tolerant control method for this class of switched systems by using average dwell-time techniques. The main features and contributions of this chapter are highlighted as follows: (1) The proposed control design works on both the switched nonlinear systems with actuator faults and its nominal systems (i.e., without actuator faults) without necessarily changing any structures and/or parameters of the proposed controllers. Therefore, it is classified as a reliable control, or passive fault-tolerant control strategy [128].

In this chapter, we study state-based and observer-based event-triggered control problems for a class of switched linear delay systems. Compared with switched non-delay systems, switched delay systems are with more complex system structure in which at least one subsystem is a delay system. The feature of this chapter lies in three aspects: (1) The event-triggered control method proposed in Chap. 2 is extended to study switched linear delay systems. Based on the different designed sampling mechanisms, two sufficient conditions of exponential stability for the closed-loop switched delay systems are obtained by using multiple Lyapunov-Krasovskii functional method and the average dwell time technique.

In this chapter, we study both state-based and observer-based output feedback event-triggered sampled-data control for a class of continuous-time switched linear systems. Compared with the result of Chap. 2, an improved event-triggered sampling mechanism is introduced, under which the controller is triggered to achieve Lyapunov stability of the closed-loop switched system combining with the average dwell time technique. A constant threshold \(\varepsilon \) is added into the proposed event-triggered sampling mechanism, the sampling period and the system performance can be improved by adjusting the value of \(\varepsilon \). Moreover, if we let \(\varepsilon =0\), the improved event-triggered sampling mechanism would degenerate into the one considered in Chap. 2. Zeno behavior can be excluded from theoretical analysis in sampling process under the improved triggering condition. Two sufficient conditions are obtained for stability of the closed-loop system by using multiple Lyapunov function method under two different feedback control approaches. The effectiveness of the proposed method is verified by a numerical example finally.

In this chapter, we present a fault-tolerant control method for the switched cascade nonlinear systems where the nonlinear subsystem contains structural uncertainties and also whose actuators are allowed to partially fail. We first define the representation of partial actuator fault models, and then find a common Lyapunov function to design a controller to asymptotically stabilize the switched systems.

In this chapter, we focus on studying the periodic sampled-data control for a class of switched linear neutral systems. By analyzing the relationship between the sampling period and the dwell time of switched system, a bond between sampling period and average dwell time is revealed to form a switching condition.

In this chapter, we aim to study the event-triggered sampled-data control problem for a class of switched linear systems. Since system states cannot be measured directly in some special situations of practical systems, see [20, 21], a state observer is first designed and then an event-triggered sampling mechanism is constructed according to the observer state.

In this chapter, we study the stabilization problem for a class of switched linear neutral systems based on a state-dependent switching strategy. A state-dependent switching strategy, which is also called hysteresis-based switching, is proposed by generalizing the min-switching strategy. A multiple generalized Lyapunov–Krasovskii functional method is proposed which allows some increase of connecting adjacent Lyapunov–Krasovskii functionals at switching points.

In this paper, the problem of state estimation for discrete-time delayed standard neural networks model (DDSNNM) is investigated. By constructing suitable Lyapunov-Krasovskii functional, the state-feedback controller is designed such that the close-loop error system is asymptotically stable. The existence condition of the state estimator was proposed in the form of linear matrix inequality, so the estimator gain matrix can be obtained easily by solving the LMI. The simulation is given to illustrate the effectiveness of our method.

In distributed optimization of multi-agent systems, agents usually cooperate to minimize a global function which is a sum of local objective functions. In this paper, distributed optimization of multi-agent systems is studied in which the global function is in a general form. A communication rule and a distributed algorithm are designed to solve the cooperative optimization problem of multi-agent systems with limited communication which is embodied by an undirected graph. The algorithm is designed according to the proposed communication rule which can share global information indirectly by transmitting information among the agents even though communications among the agents are limited, and is carried out through the true values of agents’ states instead of the estimated ones. A simulation example of distributed optimization of a four-agent system with limited communication is presented to show the effectiveness of the proposed algorithm.

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.

Both state-based and observer-based output feedback event-triggered controls for continuous-time switched linear systems are studied. An improved event-triggered sampling mechanism is adopted in feedback control, under which Zeno behaviour can be easily excluded in sampling process. Meanwhile, it is shown that the closed-loop switched system is stable in the sense of global uniform boundedness satisfying an average dwell time condition. A numerical example is finally given to verify the developed results.

The paper mainly studies the event-triggered control of switched linear systems with partially random coefficient using average dwell time switching technique. Samplings are active when a triggering condition is satisfied. On every sampling instant, new state and the switching information are transferred to controller. Compared with the zero-order holder, a dynamic controller is introduced in closed-loop to approximate the plant behavior. A sufficient condition guaranteeing stability is established by using Lyapunov function method. A related example is presented finally.

With the development of digital control technology, sampled-data control shows its prominent superiority for most practical industries. In the framework of sampled-data control, this paper studies the stabilization problem for a class of switched linear neutral systems meanwhile taking into account asynchronous switching. By utilizing the relationship between the sampling period and the dwell time of switched neutral systems, a bond between the sampling period and the average dwell time is revealed to form a switching condition, under which and certain control gains conditions exponential stability of the closed-loop systems is guaranteed. A simple example is given to demonstrate the effectiveness of the proposed method.

The paper studies the problem of asymptotically stabilizing a class of switched linear neutral systems, where none of the individual subsystems is stabilizable. A co-design of a set of candidate controllers and a hysteresis-based switching strategy is developed to achieve asymptotic stability of the closed-loop switched neutral systems. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

This paper studies feedback control for a class of switched linear systems with time delays under an event-triggered sampling control link. The sampling is determined by an event-triggered detection condition which is triggered when an error norm turns out bigger than a dynamic state norm. A sufficient solvable condition is developed which can guarantee globally exponential stability of the obtained closed-loop switched delay system. Finally, a numerical example is presented to show the effectiveness and advantage of the proposed scheme.

Cooperative optimisation problems over multi-agent systems have attracted a lot of attention. Most of existing results have been developed for the case when a cost function is given as a summation of local utilities. Instead, this study focuses on a more general case when the cost function is not given as a summation form or cannot be readily changed into a summation form. The authors call this case as the cooperative optimisation with inseparable cost functions. The authors’ basic idea is to decompose the inseparable cost function into local utilities based on geometric theory. Each of the decomposed agent optimisation problems only contains its own variable and constraints, and a gradient projection algorithm is proposed to solve the obtained distributed optimisation problem. It is further shown that the proposed algorithm converges and its solution coincides with the globally optimal solution under certain conditions, such as convexity of the cost function. Finally, two examples are given to illustrate the method.

Following the development of digital technology, controllers in many control applications are implemented on digital platforms. Although the advantages of event-triggered controllers are proposed and practical applications show their potential, relatively few theoretical results appear to study event-triggered control for switched linear systems. It is the objective of this paper to propose an event-triggered sampling mechanism and develop an observer-based dynamic output feedback control for switched systems. Compared with the existing results, a positive threshold added to the event-triggered condition guarantees that there always exist a positive lower bound ofthe minimum inter-event interval to exclude Zeno behavior. Furthermore, we present a controller design method to achieve uniform ultimate boundedness provided that average dwell time conditions of switched system are satisfied. A simulation example verifies the effectiveness of the proposed method.

The authors study the problem of asymptotically stabilising a class of switched neutral systems whose states cannot be directly measured. A state observer for each individual subsystem is constructed, based on which a switching law and a switching controller are designed. The designed switching law sufficiently considers the delayed states information. The authors adopt the multiple Lyapunov–Krasovskii functionals method to obtain a sufficient solvability condition for stabilisation which possesses less conservativeness. The authors also extend this method to stabilise switched neutral systems with time-varying structural uncertainties. Two examples are given to demonstrate the effectiveness of the authors’ proposed method.

The event-triggered control has been paid lots of attention due to its effectiveness and flexibility of reducing congestion and saving cost on designing of network control systems. However, few results have appeared on event-triggered control for switched delay systems. We thus consider the event-triggered sampling and stabilization problem for switched linear delay systems in this paper. The event considered here means the error signal exceeding a dynamic threshold. The event-triggered sampler updates and transfers the state information when an event is triggered. The switching signal is given satisfying an average dwell time condition, under which globally exponential stability of the switched delay system can be guaranteed.

Stabilization of a class of switched neutral systems with discrete time-varying delays is investigated in this paper. The upper bound of the derivative of the discrete time-varying delay is an arbitrary given unknown constant. Each subsystem is not assumed stable. In order to avoid sliding modes and chattering, a hysteresis switching law is designed based on state space partition, which considers the information of both discrete delays and neutral delays sufficiently. The obtained delay-dependent stabilization criterion is given in terms of linear matrix inequality by introducing free-weighting matrices. Finally, a simulation example is given to motivate and exemplify the proposed strategy.

This paper considers the stability and L2-gain for a class of switched neutral systems with time-varying discrete and neutral delays. Some new delay-dependent sufficient conditions for exponential stability and weighted L2-gain are developed for a class of switching signals with average dwell time. These conditions are formulated in terms of linear matrix inequalities (LMIs) and are derived by employing free weighting matrices method. As a special case of such switching signals, we can obtain exponential stability and normal L2-gain under arbitrary switching signals. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results.

In this paper, some new iterative methods for solving non-linear equations f ( x ) = 0 are presented and analyzed by means of a new two-step predictor–corrector type iterative method. The convergence criteria for these iterative methods are also discussed. Several numerical examples are given to illustrate the efficiency and performance of the new methods.

In this paper, we study the stabilization problem for a class of switched neutral systems with mixed time-varying delays under sampled-data control with fixed sampling period. The sampled control input is converted into a continuous time control with a time-varying piecewise continuous delay. We stabilize the switched systems by combining the dwell time method and the average dwell time method, and reveal a relationship between the average dwell time and the sampling period which is a necessary condition to the stabilization of the switched neutral systems.

We consider the stabilization problem of a switched delay system using sampled and quantized measurements of its state which result in finite data-rate communication. We assume that the switching is subject to the slow-switching. Each individual subsystem is assumed to be stabilizable. We derive a relationship between the number of values taken by the quantizer and the transition matrix of each individual open-loop system over one sampling period, which achieves the global asymptotic stabilization.

Dimirovski, Georgi M. (Dogus Author) -- Conference full title: ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis : July 2-4, 2012, Nantes, France The stabilization problem for a class of switched neutral systems with a discrete time-varying delay is studied in this paper. The upper bound of derivative of the discrete time-varying delay can be an arbitrary given constant which is not necessary to be less than one. Each subsystem is not assumed to be stable. A hysteresis switching law is designed based on multiple Lyapunov functionals to avoid sliding modes and chattering phenomena. The obtained delay-dependent stabilization criterion is given in terms of linear matrix inequalities (LMIs). The result is illustrated by an example.