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For switched systems that switch between distinct globally stable equilibria, we offer closed-form formulas that lock oscillations in the required neighborhood of the equilibria. Motivated by non-spiking neuron models, the main focus of the paper is on the case of planar switched affine systems, where we use properties of nested cylinders coming from quadratic Lyapunov functions. In particular, for the first time ever, we use the dwell-time concept in order to give an explicit condition for non-spiking of linear neuron models with periodically switching current. [ABSTRACT FROM AUTHOR]

Summary: The distributed convex optimization problem subject to time‐varying communication delays and switching network topologies is addressed in this paper. Based on continuous‐time Zero‐Gradient‐Sum scheme, the novel distributed algorithms are proposed to minimize the global objective function which is composed of a sum of strictly convex local cost functions. In the fixed network topology case, by constructing a new Lyapunov‐Krasovskii function, two explicit sufficient conditions for the maximum admissible time delay are derived to guarantee that all agents' states converge to the optimal solution. In the switching network topology case, the stability condition is derived by the common Lyapunov function theory. In addition, two sufficient conditions about the maximum admissible time delays are also derived for the fixed and switching weight‐balanced network topologies, respectively. Several simulation tests are used to illustrate the effectiveness of our obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new approach for the observer design of switched linear systems by ergodic theory and matrix analysis. Differently from most current results, we formulate the admissible switching sequences into a compact metric space and establish linear cocycles corresponding to the switched dynamics on this metric space under the framework of dynamical system theory. The necessary and sufficient condition for the almost surely convergent observer is given. Observer gains that minimize the unitarily invariant norm of the error dynamics during each switching process are obtained via pseudoinverse setting. An example is given to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with the problem of adaptive stabilization for a class of switched linear‐parametric nonlinear systems under arbitrary switching. The traditional adaptive backstepping control is successfully extended to switched systems from nonswitched ones where the asymptotic regulation of system state is not destroyed due to rapid or abrupt changes of switching parameters. A new switched adaptive controller is designed by exploiting a common high‐order Lyapunov function with a σ‐modification mechanism, which can reflect sufficiently the changes of plant by designing different adaptive laws and control laws for different subsystems. An explicit formula for constructing a continuous and piecewise C n − 1 virtual control function is given to remove the restriction where some C ∞ bound functions have to be constructed blindly by designers in the existing results, which may be somewhat too strict to be applied. A numerical example is provided to validate the proposed approach. [ABSTRACT FROM AUTHOR]

This paper considers the asymptotic synchronization problem for a class of uncertain complex networks (CNs) with hybrid switching and impulsive effects. The switches and impulses occur by following a time sequence which is characterized by dwell-time constraint. By designing Lyapunov function with time-varying matrix parameter, two general synchronization criteria formulated by matrix inequalities are first given, which unify synchronizing and desynchronizing impulses. Then specific conditions in terms of linear matrix inequalities (LMIs) are given by partitioning the dwell time and using convex combination technique. Compared with those criteria which are only applicable to pure synchronizing impulses or pure desynchronizing impulses, our results are more practical. It is shown that the switched impulsive CNs (SICNs) can be synchronized by desynchronizing impulses even though CNs without impulse are unsynchronized. Numerical examples are given to show the effectiveness of our new results. [ABSTRACT FROM AUTHOR]

One of the important problems in time-controlled switched dynamical systems is to find a stabilizing time sequence if there is any. The problem is challenging for switched systems with all unstable modes. Two fundamental approaches are introduced, which are classified as the fast switching method and the method of converting state-controlled signals. Five schemes are delineated and validated in the numerical study based on the two approaches. The effects of switching frequency and duty ratio on the dynamical system performance are analyzed, from which important implications have been drawn for use in practical system design. The proposed methods shall also provide intuition into understanding the mechanism of how to maintain a dynamical system’s stability when all of its modes are unstable. [ABSTRACT FROM AUTHOR]

In this paper, the event-triggered stabilisation problem for a class of switched systems with actuator saturation is investigated. Based on multiple Lyapunov function method and the average dwell time approach, a sufficient condition for exponential stability of such systems under event-triggered state-feedback controller is derived. To avoid Zeno behaviour, it is shown that there exists a positive lower bound for any two consecutive inter-event instants. Finally, two examples are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the cooperative output regulation problem for heterogeneous multi-agent systems is addressed by considering a switched leader dynamics. The switched leader dynamics consists of multiple linear models and a switching rule governing the switches among them. A switched leader is capable of generating various sophisticated reference signals for more complicated multi-agent coordination tasks. A novel distributed hybrid impulsive switching control scheme is proposed to achieve cooperative output regulation. Distributed switching stability is established using the average dwell-time technique with multiple Lyapunov functions. Moreover, the associated distributed control synthesis conditions are formulated in terms of linear matrix inequalities plus linear matrix equations. As a result, both switching rules for the leader and distributed switching protocols for the followers can be jointly synthesised via efficient semi-definite programming. An example has been used to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, a novel Lyapunov function is proposed to study switched linear systems with a switching delay between activation of system modes and activation of candidate controller modes. The novelty consists in continuity of the Lyapunov function at the switching instants and discontinuity when the system modes and controller modes are matched. This structure is exploited to construct a time-varying Lyapunov function that is non-increasing at time instants of discontinuity. Stability criteria based on the novel Lyapunov function are developed to guarantee global asymptotic stability in the noiseless case. Most importantly, when exogenous disturbances are considered, the proposed Lyapunov function can be used to guarantee a finite non-weighted L 2 gain for asynchronously switched systems, for which Lyapunov functions proposed in literature are inconclusive. A numerical example illustrates the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the semi-global cooperative output regulation problem for a class of nonlinear uncertain multi-agent systems under switching networks. At first, we study the nonadaptive case when the exosystem has no parametric uncertainties and construct a common Lyapunov function to achieve the output regulation for general switching connected networks. Next, we study the case when the exosystem contains some parametric uncertainties. To solve the problem, we establish a stability result for a class of time-varying system, which is then used in the design of distributed adaptive internal model-based control. Then we construct multiple Lyapunov functions for the switching signal with its average dwell time lower bounded by a given constant. Throughout the paper, we treat the closed-loop multi-agent system from the viewpoint of singular perturbation. In fact, the singular perturbation-based method provides an effective tool to handle the multi-agent system under switching networks. Finally, we give numerical simulations based on Duffing systems and flexible manipulator systems to illustrate the effectiveness of our method. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of continuous output-feedback stabilization for a class of switched high-order planar systems under arbitrary switchings. Based on the common Lyapunov function design method, by using the adding a power integrator technique and designing an implementable observer, a continuous output-feedback controller is constructed such that the closed-loop system is global stabilization and the output can be regulated to the origin. As an application, the developed strategy is utilized to the control design for the continuous stirred tank reactor with two modes feed stream. The simulation results verify the efficiency of the proposed design scheme. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Stability of certain classes of nonlinear time-delay switched systems is studied. For the corresponding families of subsystems, conditions of the existence of common Lyapunov–Razumikhin functions are found. The fulfilment of these conditions provides the asymptotic stability of the zero solutions of the considered hybrid systems for any switching law and for any nonnegative delay. Some examples are presented to demonstrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

A planar three-link passive–active–active (PAA) underactuated mechanical system is a kind of nonlinear system with a passive first joint. The position–posture control objective for the planar PAA system is to move the end effector from an initial position to a target position with a specified posture. This paper presents a switch control strategy to solve the position–posture control problem. First, a Lyapunov function is constructed based on the system control objective. Then, a set of main controllers based on this Lyapunov function are designed. However, the main controllers may make the system stabilise at one of equilibrium points, which is not the system target position. To avoid the above phenomenon, when the system is about to stabilise at one non-target position, the main controllers are switched to a set of sub-controllers, which are designed according to another Lyapunov function constructed based on the control objective of the active links. When the sub-controllers are running, their design parameters are adjusted to try to keep the derivative of the first Lyapunov function being a non-positive function. Therefore, the switch control between the main controllers and the sub-controllers realises the position–posture control objective of the system. Finally, the simulation results demonstrate the effectiveness of the switch control strategy. [ABSTRACT FROM AUTHOR]

The authors use Lyapunov-Krasovskii functionals to investigate the stability in probability, asymptotic stochastic stability, root-mean-square stability, and general root-mean-square exponential stability of stochastic dynamic systems of random structure with Markov switchings and perturbation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, the problems of stability and stabilization for switched systems with mode-dependent average dwell time (MDADT) switching are revisited and discussed in both continuous-time and discrete-time contexts. By introducing a class of quasi-alternative switching signals, some improved stability conditions of switched systems with MDADT are obtained. In our switching design strategy, slow switching and fast switching are, respectively, used among stable subsystems and unstable subsystems. Then, based on the stability result, stabilization conditions for switched linear systems comprising uncontrollable subsystems are presented to guarantee the underlying system to be exponentially stable. The criteria obtained for the considered switched linear systems are all provided in terms of a set of linear matrix inequalities. To illustrate the advantages of our established results, a numerical example is finally given. [ABSTRACT FROM AUTHOR]

In this paper, the problem of finite-time boundedness of switched systems in the presence of both discrete and distributed delays is addressed. The multiple Lyapunov-Krasovskii functional approach is proposed to give some criteria ensuring that the state trajectories of the system remain bounded within a finite time interval. The switching law is designed in terms of average dwell time technique and the Jensen inequality. To further reduce the conservatism, we adopt the Wirtinger inequality which encompasses the Jensen one to derive a new condition. Finally, two numerical examples are presented to demonstrate the effectiveness of our result and the potential of employing the Wirtinger inequality. [ABSTRACT FROM AUTHOR]

This paper investigates finite-time stabilization ( FTS ) problem for a class of cascade nonlinear switched systems. Unlike the existing approach based on time-dependent switching strategy, in which the switching instants must be given in advance, largest region function strategy, i.e., state-dependent switching strategy, is adopted to design the switching signal. Based on multiple Lyapunov-like functions method, sufficient conditions for FTS of cascade nonlinear switched systems are derived and the corresponding sliding motion problems are also considered. Finally, an example is given to illustrate the applicability and the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses a stochastic SIS epidemic model with vaccination under regime switching. The stochastic model in this paper includes white and color noises. By constructing stochastic Lyapunov functions with regime switching, we establish sufficient conditions for the existence of a unique ergodic stationary distribution. [ABSTRACT FROM AUTHOR]

Robust stabilisation andL2-gain analysis for a class of switched systems with actuator saturation are studied in this paper. The switching signal of the controllers lags behind that of the system modes, which leads to the asynchronous switching between the candidate controllers and the subsystems. By combining the piecewise Lyapunov function method with the convex hull technique, sufficient conditions in terms of LMIs for the solvability of the robust stabilisation and weightedL2-gain problems are presented respectively under the dwell time scheme. Finally, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper is concerned with theH∞filtering problem for a class of continuous-time linear switched systems with the asynchronous behaviours, where ‘asynchronous’ means that the switching of the filters to be designed has a lag to the switching of the system modes. By using the Lyapunov-like functions and the average dwell time technique, a sufficient condition is obtained to guarantee the asymptotic stability with a weightedH∞performance index for the filtering error system. Moreover, the results are formulated in the form of linear matrix inequalities that are numerical feasible. As a result, the filter design problem is solved. Finally, an illustrative numerical example is presented to show the effectiveness of the results. [ABSTRACT FROM AUTHOR]

This paper considers the stabilisation of switching nonlinear models by switching between the subsystems. We assume that arbitrary switching between two subsystems is possible once a subsystem has been active for a predefined number of samples. We use a Takagi–Sugeno representation of the models and a switching Lyapunov function is employed to develop sufficient stability conditions. If the conditions are satisfied, we construct a switching law that stabilises the system. The application of the conditions is illustrated in several examples. [ABSTRACT FROM AUTHOR]

This paper studies practical output tracking of switched nonlinear systems inp-normal form. No solvability of the practical output tracking problem for subsystems is required. A constructive scheme to solve the problem for a switched nonlinear system is set up by exploiting the single Lyapunov function method and the tool of adding a power integrator. Also, we design a proper switching law and construct state-feedback controllers of subsystems. A two inverted pendulums as a practical example, which cannot be handled by the existing approaches, illustrates our theoretical result. [ABSTRACT FROM PUBLISHER]

This paper studies robust stability of positive switched systems (PSSs) with polytopic uncertainties in both discrete-time and continuous-time contexts. By using multiple linear copositive Lyapunov functions, a sufficient condition for stability of PSSs with dwell time is addressed. Being different from time-invariant multiple linear copositive Lyapunov functions, the Lyapunov functions constructed in this paper are time-varying during the dwell time and time-invariant afterwards. Then, robust stability of PSSs with polytopic uncertainties is solved. All conditions are solvable via linear programming. Finally, illustrative examples are given to demonstrate the validity of the proposed results. [ABSTRACT FROM PUBLISHER]

This paper investigates the finite-time filter design problem for a class of switched linear systems with parameter uncertainties and impulsive effects. The sensor failures with output-measurement errors and mode-detection delays are taken into account. A filter mode-dependent Lyapunov-like function construction approach is developed which can effectively reduce the filter design difficulty induced by the mode-detection delays. Sufficient conditions on finite-time boundedness and finite-time H ∞ performance are first derived for the augmented switched error systems, upon which the mode-dependent finite-time H ∞ filter is designed. Performance of the potential of the developed filter is illustrated by a numerical example and an application to PWM (Pulse-Width-Modulation)-driven boost converter. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the consensus problem for leaderless and leader–followers multi-agent systems with periodically intermittent control. The dynamics of each agent in the system is a linear system, and the interconnection topology among the agents is assumed to be switching. We assume that each agent can only share the outputs with its neighbours. Therefore, a class of distributed intermittent observer-based consensus protocols are proposed for each agent. First, in order to solve this problem, a parameter-dependent common Lyapunov function is constructed. Using this function, we prove that all agents can access a prescribed value, under the designed intermittent controller and observer, if there are suitable conditions on communication. Second, based on the investigation of the leader-following consensus problem, we design a new distributed intermittent observer-based protocol for each following agent. Finally, we provide an illustrative example to verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, distributed leader-following consensus for a class of nonlinear multi-agent systems with switching topologies and unreliable communications is studied. Each possible topology contains a directed spanning tree rooted at the leader. Agents share the information only with their neighbors on some disconnected time intervals due to the unreliable communications. By designing suitable distributed controllers, all follower nodes asymptotically synchronize to the leader node if the communication rate is larger than a threshold value for each time interval. By using multiple Lyapunov functions theory and linear matrix inequalities technique, some sufficient conditions are given to guarantee the consensus. Moreover, based on the theoretical results, the admissible communication rate and convergence rate of the whole systems are adjusted by the feedback gain matrix, which provides helpful design guidelines in practical applications. Finally, a simulation example is given to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper deals with the design of anti-windup compensator for discrete-time switched systems subject to input saturation. The cases of static and dynamic anti-windup controllers are addressed aiming at maximising the estimate of the basin of attraction of the origin for the closed-loop system. Two aspects of the switching law are taken into account during the design: either it is arbitrary or it is a part of the complete control law. Theoretical conditions allowing to synthesise the anti-windup compensator are mainly described through linear matrix inequalities. Computational oriented conditions are then provided to solve convex optimisation problems that are able to give a constructive solution. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of observed-based event-triggered control for switched linear systems with time-varying delay and exogenous disturbance. First by employing a state observer, an observer-based event-triggered controller is designed to guarantee the finite-time boundedness and finite-time stabilization of the resulting dynamic augmented closed-loop system. Then based on the Lyapunov-like function method and the average dwell time technique, some sufficient conditions are given to ensure the finite-time boundedness and finite-time stabilization, respectively. Furthermore, the lower bound of the minimum interevent interval is proved to be positive, which thus excludes the Zeno behavior of sampling. A numerical example is finally exploited to verify the effectiveness and potential of the achieved control scheme. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of robust state estimation for a class of switched linear systems with unknown inputs under average dwell time (ADT) switching, where the switching of the observers is synchronous with that of the estimated system. First, based on the feasibility of an optimization problem with linear matrix inequality (LMl) constraint, a robust sliding-mode switched observer is developed such that the asymptotic state reconstruction is guaranteed even if the switched system is with unknown inputs. Second, a reduced-order switched system which avoids the influence of unknown inputs is constructed by the technique of state transformation, and a reduced-order switched observer is proposed to estimate the continuous states of the original switched system. Next, the conditions under which a full-order switched observer exists also guarantee the existence of a reduced-order switched observer. The convergence of the state estimate is proved to be exponential by appropriate Lyapunov analysis. Finally, the simulation results confirm the predicted performance and applicability by a simplified three-tank system. [ABSTRACT FROM AUTHOR]

This paper revisits the problem of enlarging the domain of attraction of a linear system with multiple inputs subject to actuator saturation by designing a switching anti-windup compensator. The closed-loop system consisting of the plant, the controller and the anti-windup compensator is first equivalently formulated as a linear system with input deadzone. We then partition the input space into several regions. In one of these regions, all inputs saturate with the time-derivative of the saturated input being zero. In each of the remaining regions, there is a unique input that does not saturate. The time derivative of the deadzone function associated with the unsaturating input is zero. By utilizing these special properties of the inputs on an existing piecewise Lyapunov function of the augmented state vector containing the deadzone function of inputs, we design a separate anti-windup gain for each region of the input space. The switching from one anti-windup gain to another is activated when the input signals leave one region for another, which can be implemented online since only the measurement of the input signals is required. Simulation results indicate that the proposed approach has the ability to obtain a significantly larger estimate of the domain of attraction than the existing approaches. [ABSTRACT FROM AUTHOR]

This paper concerns the synchronization problem of complex networks with the random switching topologies. By modeling the switching of network topologies as a Markov process, a novel event-triggered synchronization strategy is proposed. Unlike the existing strategies, the event detection of this strategy only works at the network topology switching time instant, which can significantly decrease the communication frequency between nodes and save the network resources. Under this strategy, the synchronization problem of complex network is equivalently converted to the stability of a class of Markovian jump systems with a time-varying delay. By using the Lyapunov–Krasovskii functional method and the weak infinitesimal operation, a sufficient condition for the mean square synchronization of the complex networks subject to Markovian switching topologies is established. Finally, a numerical simulation example is provided to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of finite-time sampled-data control for switching T–S fuzzy systems. By using the input delay approach, the switching T–S fuzzy systems with variable sampling is transformed into a continuous-time switching T–S fuzzy systems with state-delay. A novel Lyapunov functional is proposed to deal with the problems of finite-time stability (FTS) and finite-time stabilization. Based on the constructed Lyapunov functions and minimum dwell time (MDT) method, new FTS conditions are derived for switching T–S fuzzy systems. Then, according to the FTS conditions, a detailed procedure for designing local sampled-data controllers is given. Finally, an example is provided to illustrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive fault tolerant controller design is proposed for a class of nonlinear unknown systems with multiple actuators. The controller consists of an adaptive learning-based control law, a Nussbaum gain, and a switching function scheme. The adaptive control law is implemented by a two-layer neural network to accommodate the unknown system dynamics. Without the requirement of additional fault detection mechanism, the switching function is designed to automatically locate and turn off the unknown faulty actuators by observing a control performance index. The asymptotic stability of the system output in the presence of actuator failures is rigidly proved through standard Lyapunov approach, while the other signals of the closed-loop system are guaranteed to be bounded. The theoretical result is substantiated by simulation on a two-tank system. [ABSTRACT FROM AUTHOR]

This study considers the functional observers design for a class of discrete-time switched singular systems simultaneously subject to state delays, unknown inputs (UIs) and arbitrary switching sequences. The singular matrix E is assumed to be switching-mode-dependent, and the UIs are present in both the state and the measurement channels. A mode-dependent, delay-type observer is first constructed, then, based on the unknown input decoupling and the switched Lyapunov theory, a method is proposed to design such observer which ensures both: the total elimination of the UIs and exponential estimate of the given function of the state vector. The conditions for the existence of the proposed observer are given through algebraic matrix inequalities, and exponential stability of the observation error dynamics is derived by using a properly constructed decay-rate-dependent switched Lyapunov function and the linear matrix inequality technique. Finally, an illustrative example is given to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates the problems ofL1-gain analysis and control synthesis of positive switched systems. Linear supply rates andL1-gain notations are introduced to analyse the performance of the underlying systems. Stability with a weightedL1-gain for autonomous systems are solved by using multiple linear copositive Lyapunov functions incorporated with the average dwell time approach. Then, state-feedback and output-feedback controllers are designed to guarantee the stabilisation with a weightedL1-gain for non-autonomous systems. All present conditions are solvable in terms of linear programming. Finally, a practical example is given to illustrate the validity of theoretical findings. [ABSTRACT FROM PUBLISHER]

A new method with an efficient algorithm is developed for computing the Lyapunov constants of planar switching systems, and then applied to study bifurcation of limit cycles in a switching Bautin system. A complete classification on the conditions of a singular point being a center in this Bautin system is obtained. Further, an example of switching systems is constructed to show the existence of 10 small-amplitude limit cycles bifurcating from a center. This is a new lower bound of the maximal number of small-amplitude limit cycles obtained in quadratic switching systems near a singular point. [ABSTRACT FROM AUTHOR]

In this article, the [ABSTRACT FROM AUTHOR]

This paper proposes a novel reconstruction procedure to lessen the conservatism of stability assurance of T-S Fuzzy Mode. By dividing the state variables into some bounded regions, the considered T-S fuzzy model can be first transferred to an alternative form via a reconstructing procedure. Thus, we can attain some relaxing stability criteria based on the switching quadratic Lyapunov function (SQLF) method. Notably, these proposed conditions are explicitly formulated by linear matrix inequality (LMI) form and can handily be evaluated by current software tools. Finally some illustrative examples are given to experimentally demonstrate the validity and merit of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the fault detection (FD) problem for a class of linear discrete-time switched systems in finite-frequency domain. The fault detection filters (FDFs) with switching mechanism are utilized to generate residual to detect fault. Different from the existing FD schemes based on the arbitrary switching or average dwell time switching method, a novel scheme is presented, where the states of the FDFs are used to construct not only the residual but also the switching law. This guarantees that the overall switched system is asymptotically stable and with the fault sensitive performance and disturbance attenuation performance in the low-, middle-, and high-frequency domain, respectively. A solution of the considered problem is given via linear matrix inequalities. Finally, a numerical example is presented to show the advantage of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the convergence domain for time-varying switched systems. We construct multiple Lyapunov functions and each Lyapunov function is decreasing outside a ball whose radius is time-varying. We give a relatively accurate convergence domain for a general time-varying switched system. Finally, a numerical example, a mass–spring–damper system, is provided to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we propose the sliding mode control (SMC) based on the fuzzy disturbance observer for systems with disturbances to minimize the switching gain and reduce chattering phenomenon. The proposed method exhibits the following two attractive features. First, using the universal approximation and the adjustable parameter of the fuzzy system, the switching gain in proposed control law is only required to be designed greater than the sum of magnitude of the disturbance approximation error and the fuzzy reconstruction. It implies that the proposed controller is less dependent on the range of switching gain to stabilize the system than SMC; thus, the minimization of switching gain can reduce the chattering. Second, the proposed method exhibits much better control performance than the traditional SMC and Nonlinear Disturbance Observer (NDOB)-based SMC, such as reduced chattering and good performance. The stability of the proposed control system is proved using Lyapunov method. To verify the effectiveness of the minimization of switching gain and chattering, we show the performance of the proposed method through some simulations of the inverted pendulum. [ABSTRACT FROM AUTHOR]

This paper is mainly concerned with the problem of global output feedback stabilization for a class of switched nonlinear systems with uncertain control coefficients. First of all, it is shown that the unknown control coefficients are lumped together via a common coordinate transformation, thus the original switched nonlinear system is transformed into a new switched system for which control design is feasible. Second, by constructing a common Lyapunov function relying on the designed state observer, the common output feedback controller independent of switching signals is designed based on the backstepping method so as to guarantee the global asymptotic stability of the resulting closed-loop switched system under arbitrary switchings. Two examples are included for verifying the effectiveness of the method proposed. [ABSTRACT FROM AUTHOR]

We are concerned with the stability problem for linear discrete-time switched systems with time delays. The problem is solved by using multiple Lyapunov functions to develop constructive tools for the exponential stability analysis of the switched time-delay system. Furthermore, the uncertainties of the switched systems are also taken into consideration. Sufficient delay-dependent conditions are derived in terms of the average dwell time for the exponential stability based on linear matrix inequalities (LMIs). Finally, numerical examples are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

SUMMARY On the basis of a linear copositive Lyapunov function (LF) and a diagonal quadratic LF, respectively, two slow stabilizing switching laws are proposed for discrete time positive switched systems composed of [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper considers the stabilization problem for a class of cascade switched nonlinear systems. Each subsystem of the switched nonlinear system studied consists of a linear part and a nonlinear part, and the linear parts are composed of stabilizable and unstabilizable subsections. The actuator saturation is taken into consideration using the convex hull technique. Through constructing the proper Lyapunov functions, sufficient conditions in terms of LMIs for the solvability of the stabilization problem are presented. A state feedback controller and the dwell-time switching strategy are proposed to guarantee the exponential stability of the resulting closed-loop system. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Abstract: The synchronization problem of a neutral complex dynamical network (NCDN) with distributed delay, Markovian jump parameters and partially unknown transition rates via sampled-data controller is investigated in this paper. The retarded, neutral and distributed delays are considered to be interval mode-dependent and time-varying, while the sampling period is assumed to be time-varying and bounded. By the interval dividing approach, a new augmented stochastic Lyapunov functional is constructed, which contains some triple-integral terms to reduce the conservativeness. Then the delay-range-dependent and rate-dependent exponential stability conditions for the closed-loop error system are obtained by the Lyapunov–Krasovskii stability theory, integral matrix inequalities and reciprocally convex lemma. Based on these new stability conditions, the sampled-data exponential synchronization controllers are found in terms of the solutions to linear matrix inequalities. Finally, numerical examples are given to demonstrate the feasibility and effectiveness of the proposed theoretic result. [Copyright &y& Elsevier]