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1.
This paper studies vector incremental L2-gain and incremental stability for switched nonlinear systems using individual incremental gains and multiple storage functions. Firstly, a vector incremental L2-gain concept for switched nonlinear systems is proposed. Each subsystem is not required to have incremental L2-gain, but it has its own incremental L2-gain and the related storage function, when it is active. The transformation of “energy” from the active subsystem to each inactive subsystem is characterized by cross-supply rates. Then, we show that a switched nonlinear system who has vector incremental L2-gain can be incrementally stabilized under some constraints on the energy change of inactive subsystems. Secondly, a state-dependent switching law is designed to achieve vector incremental L2-gain, even if each subsystem does not have incremental L2-gain in the classic sense. Thirdly, each switched system is not required to have vector incremental L2-gain, but the feedback interconnection of switched nonlinear systems is incrementally stabilized by the design of a composite switching law. The switching law allows the two switched systems switch asynchronously. Two examples are provided to verify the effectiveness of the proposed method.  相似文献   

2.
In this paper, the stability, L1-gain analysis and asynchronous L1-gain control problems of uncertain discrete-time switched positive linear systems (DSPLSs) with dwell time are investigated. First, several convex and non-convex conditions on dwell time stability of DSPLSs with interval and polytopic uncertainties are presented, and the relation between these conditions is revealed. Then, via a switched dwell-time-dependent co-positive Lyapunov functions (SDTLFs) approach, convex sufficient conditions on L1-gain analysis and asynchronous L1-gain control of DSPLSs with interval uncertainties are derived. Meanwhile, via the switched parameter-dwell-time-dependent co-positive Lyapunov functions (SPDTLFs) approach, the L1-gain analysis and asynchronous L1-gain controller design problems of DSPLSs with polytopic uncertainties are also solved. The stability and L1-gain analysis results are given in terms of linear programming (LP). The controller design results are presented in terms of bilinear programming (BP), which can be solved with the help of iterative algorithm. At last, both numerical and practical examples are provided to show the effectiveness of the results.  相似文献   

3.
This paper investigates L1-gain analysis and control of impulsive positive systems (IPSs) with interval uncertainty and time delay. For different types of impulsive effect, by means of the Razumikhin techniques and Lyapunov function theory, conditions are developed for guaranteeing the robust exponential stability with L1-gain performance. Then the positive stabilization with L1-gain performance is also addressed for IPSs with interval uncertainty and time delay through the state feedback control. In addition, the way to explore the minimum L1-gain is discussed. All the obtained conditions can be easily inspected by the linear programming (LP) method when some parameters are preset. Finally, simulations are provided to demonstrate the validity of the theoretical results.  相似文献   

4.
This paper is concerned with the exponential stability and L1-gain analysis problem for switched positive T–S fuzzy systems under both time-varying delays and asynchronous switching. By permitting the increase of the designed multiple Lyapunov functionals during the running time of the activated subsystem, solvable conditions for the stability and L1-gain are developed by adopting the mode-dependent average dwell time (MDADT) technique. The desired controllers guaranteeing the stability and the L1-gain performance are designed based on the obtained solvable conditions. An example is given to demonstrate the effectiveness of the proposed methods.  相似文献   

5.
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.  相似文献   

6.
This paper investigates the standard H∞ performance for a class of switched linear systems with time-varying delay in the framework of the delay-dependent/delay-independent minimum dwell time. For the studied systems, we first construct two types of multiple time-varying Lyapunov functionals, and then obtain the sufficient conditions by restricting the decay of the Lyapunov functional of the active subsystem and forcing “energy” of the overall switched system to decrease at switching instants by the proposed Lyapunov functionals to guarantee standard L2-gain performance meanwhile ensuring their internal stability with minimum dwell time switching. Finally, two examples are presented to illustrate the effectiveness of the proposed results.  相似文献   

7.
This paper is devoted to the characterization of L∞-gain for positive singular systems with time-varying delays. First, we introduce an augmented system to replace the original system in order to analyze the positivity of singular systems with time-varying delays. By investigating the monotonicity of state trajectory, the L∞-gain for singular system with constant delays is characterized. Then, by comparing the trajectories of time-varying delay system and constant delay case, we finally propose the L∞-gain for singular system with time-varying delays. It is shown that the L∞-gain of positive singular systems is independent of the magnitude of delays.  相似文献   

8.
We study the input-to-state stability (ISS) of switched nonlinear input delay systems under asynchronous switching. Our results apply to cases where some subsystems of the switched systems are not necessarily stable under the influence of input delay. By making a compromise among the matched-stable period, the matched-unstable period, and the unmatched period and allowing the increase of the Lyapunov–Krasovskii functional (LKF) on all the switching times, the extended stability criteria for switched delay systems in generally nonlinear setting are derived first. Then, we focus on switched nonlinear input delay systems where the presence of the input delay leads to the instability of some subsystems of it. By explicitly constructing input-to-state stable LKF, the sufficient conditions for ISS of switched nonlinear input delay systems under asynchronous switching are presented. Finally, two examples are given to illustrate the effectiveness of the proposed theory.  相似文献   

9.
In this paper, we investigate the incremental H∞ performance problem for a class of stochastic switched nonlinear systems by using a state-dependent switching law and the maximum and minimum dwell time approach. By resorting to the state-dependent switching law, some sufficient conditions are provided to cope with the incremental H∞ performance problem, which can be applied even if all subsystems are unstable. Then, based on the maximum and minimum dwell time scheme, the incremental H∞ performance problem to be solvable is derived for two cases: one is all subsystems are incrementally globally asymptotically stable in the mean(IGASiM), another is both IGASiM subsystems and unstable subsystems coexist. When all subsystems are IGASiM, the stochastic switched nonlinear system is IGASiM and possesses a incremental L2-gain under given conditions. When both IGASiM subsystems and unstable subsystems coexist, if the activation time ratio between IGASiM subsystems and unstable ones is not less than a specified constant, the sufficient conditions for the incremental H∞ performance of the stochastic switched nonlinear system are given. Two numerical examples are given to illustrate the validity of methods proposed.  相似文献   

10.
In this paper, we consider the H∞ hybrid dynamical output-feedback control problem for discrete-time switched linear systems under asynchronous switching. A time-varying multiple Lyapunov-like-function (MLF) approach is applied to derive sufficient conditions that guarantee the stability and weighted l2-gain performance of the closed-loop systems, where the established conditions explicitly depend on the upper and lower bounds of asynchronous switching delays. An alternative approach is proposed to decouple the bilinear problems of the control synthesis conditions. Convex optimization algorithms are also proposed based on the established conditions to determine the minimum l2-gain performance. Two numerical examples are provided to illustrate the effectiveness of the proposed method, demonstrating significant improvement over the existing results.  相似文献   

11.
This paper concentrates on the output tracking control problem with L1-gain performance of positive switched systems. We adopt the multiple co-positive Lyapunov functions technique and conduct the dual design of the controller and the switching signal. Through introducing a new state variable, which is not the output error, the output tracking control problem of the original system is transformed into the stabilization problem of the dynamics system of this new state. The proposed approach is still effective even the output tracking control problem of any subsystem is unsolvable. According to the state being available or not, we establish the solvability conditions of the output tracking control problem for positive switched systems, respectively. In the end, a number example demonstrates the validity of the presented results.  相似文献   

12.
This paper considers the sampled-data distributed H∞ control problem for 1-D semilinear transport reaction equations with external disturbances. It is assumed that a finite number of point spatial state measurements are available. A Razumikhin-type approach is developed for stability and L2-gain analysis of the closed-loop system. In contrast to Halanay?s inequality based approach, the proposed Razumikhin-type approach not only provides a subtle decay estimate of the selected Lyapunov functional, but also guarantees the H∞ performance index to be negative if certain conditions are satisfied. By introducing a time-dependent Lyapunov functional combined with the use of Wirtinger?s inequality, sufficient conditions for the internal exponential stability and finite L2-gain are derived in terms of linear matrix inequalities. The obtained conditions establish a quantitative relation among the upper bounds on the spatial sampling intervals and the time sampling intervals, and L2-gain. Two numerical examples are provided to illustrate the usefulness of the proposed theoretical results.  相似文献   

13.
This paper is concerned with the H∞ control problem for a class of networked control systems (NCSs) with time-varying delay that is less than one sampling period. By applying a new working mode of the actuator and considering state feedback controllers, a new discrete-time switched system model is proposed to describe the NCS. Based on the obtained switched system model, a sufficient condition is derived for the closed-loop NCS to be exponentially stable and ensure a prescribed H∞ performance level. The obtained condition establishes relations among the delay length, the delay variation frequency, and the system performances of the closed-loop NCS. Moreover, a convex optimization problem is formulated to design the H∞ controllers which minimize the H∞ performance level. An illustrative example is given to show the effectiveness of the proposed results.  相似文献   

14.
Finite-time stability concerns the boundness of system during a fixed finite-time interval. For switched systems, finite-time stability property can be affected significantly by switching behavior; however, it was neglected by most previous research. In this paper, the problems of finite-time stability analysis and stabilization for switched nonlinear discrete-time systems are addressed. First, sufficient conditions are given to ensure a class of switched nonlinear discrete-time system subjected to norm bounded disturbance finite-time bounded under arbitrary switching, and then the results are extended to H∞ finite-time boundness of switched nonlinear discrete-time systems. Finally based on the results on finite-time boundness, the state feedback controller is designed to H∞ finite-time stabilize a switched nonlinear discrete-time system. A numerical design example is given to illustrate the proposed results within this paper.  相似文献   

15.
This paper studies the problems of stability and H∞ model reference tracking performance for a class of asynchronous switched nonlinear systems with uncertain input delay. First, it is assumed switched controller and corresponding piecewise Lyapunov function are unknown but the derivative of piecewise Lyapunov function has a condition; this condition implies that the nominal system (system without input delay and disturbance) is exponentially stable by any switched controller which satisfies this condition. With this assumption, a proper Lyapunov–Krasovskii functional is constructed. By employing this new functional and average dwell time technique, the delay-dependent input-to-state stability criteria are derived under a certain delay bound; in addition, a mechanism which finds the upper bound of input delay is proposed. Finally, a kind of state feedback control law which fulfils condition of aforesaid piecewise Lyapunov function is introduced to guarantee the input-to-state stability and H∞ model reference tracking performance. Simulation examples are presented to demonstrate the efficacy of results.  相似文献   

16.
In this paper, a new memory-based control problem is addressed for neutral systems with time-varying delay, input saturations and energy bounded disturbances. Attention is focused on the design of a memory-based state feedback controller such that the closed-loop system achieves the desirable performance indices including the boundedness of the state trajectories, the H∞ disturbance rejection/attenuation level as well as the asymptotic stability. By using the combination of a novel delay-dependent polytopic approach, augmented Lyapunov–Krasovskii functionals and some integral inequalities, delay-dependent sufficient conditions are first proposed in terms of linear matrix inequalities. Then, three convex optimization problems are formulated whose aims are to, respectively, maximize the disturbance tolerance level, minimize the disturbance attenuation level and maximize the initial condition set. Finally, simulation examples demonstrate the effectiveness and benefits of the obtained results.  相似文献   

17.
《Journal of The Franklin Institute》2019,356(17):10296-10314
This paper investigates the problem of distributed event-triggered sliding mode control (SMC) for switched systems with limited communication capacity. Moreover, the system output and switching signals are both considered to be sampled by distributed digital sensors, which may cause control delay and asynchronous switching. First of all, a novel distributed event-triggering scheme for switched systems is proposed to reduce bandwidth requirements. Then, a state observer is designed to estimate the system state via sampled system output with transmission delay. Based on the observed system state, a switched SMC law and corresponding switching law are designed to guarantee the exponential stability of the closed-loop system with H∞ performance. Finally, an application example is given to illustrate the effectiveness of the proposed method.  相似文献   

18.
In this paper, the problem of state and unknown input estimations for a class of discrete-time switched linear systems with average dwell time switching is investigated. First, a proportional integral observer with an exponential H∞ performance is constructed to estimate the system state and unknown input simultaneously. Second, both of the observability and the stability of the estimation error system are analyzed, then the derivation of the observer gain matrices is transformed into the calculation of linear matrix inequalities. Third, the obtained results are extended to the systems with output disturbances. Finally, two simulation examples are provided to show the validity and effectiveness of the proposed methods.  相似文献   

19.
This paper concerns the simultaneous fault detection and control (SFDC) problem for a class of nonlinear stochastic switched systems with time-varying state delay and parameter uncertainties. The switching signal of detector/controller unit (DCU) is assumed to be with switching delay, which results in the asynchronous switching between the subsystems and DCU. By constructing a switching strategy depending on the state and switching delays, new sufficient conditions expressed by a set of linear matrix inequalities (LMIs) is derived to design DCU gains. This problem is formulated as an H∞ optimization problem and both mean square exponential stability and fault detection of augmented system are considered. A numerical example is finally exploited to verify the effectiveness and potential of the achieved scheme.  相似文献   

20.
This paper is concerned with the stability analysis of discrete-time linear systems with time-varying delays. The novelty of this paper lies in that a novel Lyapunov–Krasovskii functional that updates periodically along with the time is proposed to reduce the conservatism and eventually be able to achieve the non-conservativeness in stability analysis. It can be proved that the stability of a discrete-time linear delay system is equivalent to the existence of a periodic Lyapunov–Krasovskii functional. Two necessary and sufficient stability conditions in terms of linear matrix inequalities are proposed in this paper. Furthermore, the novel periodic Lyapunov–Krasovskii functional is employed to solve the ?2-gain performance analysis problem when exogenous disturbance is considered. The effectiveness of the proposed results is illustrated by several numerical examples.  相似文献   

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