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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]

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]

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]

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]

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 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]