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1.
In this note, we will devote to investigate the stability of discrete-time switched positive linear time-varying systems (PLTVSs). Firstly, a new asymptotic stability criterion of discrete-time PLTVSs is obtained by using time-varying copositive Lyapunov functions (TVCLFs) and this criterion is then extended to the switched case based on the multiple TVCLFs. Furthermore, the sufficient conditions are derived for stability of discrete-time switched PLTVSs with stable subsystems by means of function-dependent average dwell time and function-dependent minimum dwell time. In addition, the stability sufficient conditions are drawn for the switched PLTVSs which contain unstable subsystems. It is worth noting that the difference of TVCLFs and multiple TVCLFs are both relaxed to indefinite in our work. The theoretical results obtained are verified by two numerical examples.  相似文献   

2.
The stability and stabilization synthesis problems of the switched positive systems (SPSs) with external disturbances are studied in this paper. For the studied SPSs, a weighted mode-dependent average dwell time (WMDADT) switched strategy has been adopted to analyze the above-mentioned issue, based on which the deficiencies of the existing ADT and MDADT switching techniques can be overcomed. By using the adopted strategy, some improved stability conditions that have less conservativeness are presented for the systems under investigation. Moreover, based on the developed stability conditions, an efficient controller design method avoiding computational complexity and eliminating the rank requirement of the controller is presented. In the end, the effectiveness of the method is verified by two numerical examples.  相似文献   

3.
In this paper, we deal with the finite-time stability of positive switched linear time-delay systems. By constructing a class of linear time-varying copositive Lyapunov functionals, we present new explicit criteria in terms of solvable linear inequalities for the finite-time stability of positive switched linear time-delay systems under arbitrary switching and average dwell-time switching. As an important application, we apply the method to finite-time stability of linear time-varying systems with time delay.  相似文献   

4.
This paper addresses the existence of a common linear copositive Lyapunov function for discrete-time switched positive systems. Our results reveal that the existence of such a function is equivalent to the Schur stability of a kind of special matrices, these matrices consist of column vector of system matrices in an appropriate manner. A simple example is provided to illustrate the implication of our results.  相似文献   

5.
Logical network is a special kind of positive systems with finite state space and logical operations. This paper analyzes the robust stability of switched delayed logical networks (SDLNs) with all unstable modes. The main mathematical tool is the semi-tensor product of matrices, which is used to convert the dynamics of SDLNs with all unstable modes into an equivalent algebraic state space representation. Following the algebraic state space representation framework, the concept of robustly stable parts is proposed, based on which, a new criterion is established for the robust stability of SDLNs with all unstable modes. Finally, two examples are given for the verification of main results.  相似文献   

6.
This paper is concerned with exploring less conservative stability conditions for a class of switched positive linear systems. A switched matrix-parameterized copositive Lyapunov function (SMPCLF) is first introduced, where “matrix-parameterized” implies that the parameters of the constructed Lyapunov function are distributed in a matrix, which is different from the traditional vector-parameterized copositive Lyapunov function. Based on the proposed SMPCLF, a new stability criterion is derived for the underlying systems under arbitrary switching. Furthermore, by performing higher order relaxations in the SMPCLF and its time difference by positive states, the conservativeness can be further reduced. A numerical example is given to demonstrate the effectiveness and advantages of the obtained theoretical results.  相似文献   

7.
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8.
Unlike many papers focusing on common linear copositive Lyapunov functions (CLCLFs) for positive switched systems, this paper studies the existence of a class of common weak linear copositive Lyapunov functions called common joint linear copositive Lyapunov functions (CJCLFs). Necessary and sufficient conditions for the existence of CJCLFs are established. The conditions are easily verifiable via the straightforward computation, and can be applied to the asymptotic stability problem of the positive switched linear system when each switching mode is only Lyapunov stable.  相似文献   

9.
The stability issue of discrete-time switched systems governed by cyclic switching laws is discussed in this paper. By establishing inverse-timer-based multiple Lyapunov functions (ITBMLFs), which are less conservative than traditional MLFs, limitations of the existing findings on discrete-time cyclic switched systems (DTCSSs) are well relaxed. Furthermore, from the perspective of computational complexity adjustment, the proposed ITBMLFs are confirmed to be more flexible than the previous ones, which is especially meaningful for the DTCSSs consisting of a large number of subsystems. Based on the cycle-dependent average dwell time (CD-ADT) concept and the ITBMLF approach, newly enhanced stability conditions are launched for DTCSSs where subsystems can be entirely or partially stable, or even completely unstable. Moreover, robust stability of DTCSSs can be achieved when norm-bounded and time-varying parameter uncertainties (NBTVPUs) are taken into account. Finally, the effectiveness and superiority of the proposed technologies are expounded through numerical examples.  相似文献   

10.
The saturated control problem is investigated for positive switched Takagi–Sugeno (T–S) fuzzy systems with partially controllable subsystems in this paper. Based on the parallel distribution compensation (PDC) algorithm and the convex hull technology, new fuzzy control schemes are proposed for continuous-time positive switched T–S fuzzy systems (PSTSFSs) with actuator saturation. By the multiple linear co-positive Lyapunov function and the slow-fast combined mode-dependent average dwell time (MDADT) approach, sufficient conditions for the stability of continuous-time closed-loop PSTSFSs are developed, which is an extension of the results in previous literature. Furthermore, the least conservative estimation of the attraction domain of PSTSFSs is transformed into an optimization problem. Finally, three simulation examples are given to illustrate the effectiveness of the proposed saturated control schemes.  相似文献   

11.
This paper investigates the finite-time stabilization for a class of upper-triangular switched nonlinear systems, where nonlinearities are allowed to be lower-order growing. Due to the special structure of the considered system, the presented methods for lower-triangular switched nonlinear systems in the literature can not be directly utilized. To solve the problem, a state feedback control law with a new structure is designed to guarantee the global finite-time stability of the closed-loop system under arbitrary switching signals by using the recursive design approach and the nested saturation method. A simulation example is provided to show the effectiveness of the proposed method.  相似文献   

12.
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   

13.
This paper investigates hybrid observer design of a class of unknown input switched nonlinear systems. The distinguishing feature of the proposed method is that the stability of all subsystems of the error switched systems is not necessarily required. First, an output derivative-based method and time-varying coordinate transformation are considered to eliminate the unknown input. Then in order to maintain a satisfactory estimation performance, an impulsive full-order and switched reduced-order observer are developed with a pair of upper and lower dwell time bounds and constructing time-varying Lyapunov functions combined with convex combination technique. In addition, the time-varying Lyapunov functions method is also used to analyze the stability of a class of error switched nonlinear systems with stable subsystems. Finally, two examples are presented to demonstrate the effectiveness of the proposed method.  相似文献   

14.
In this paper, the stability problem of discrete-time systems with time-varying delay is considered. Some new stability criteria are derived by using a switching technique. Compared with the Lyapunov–Krasovskii functional (LKF) approach, the method used in this paper has two features. First, a switched model, which is equivalent to the original system and contains more delay information, is introduced. It means that the criteria obtained by using the LKF method can be regarded as stability criteria for the switched system under arbitrary switching. Second, when the switching signal is known, the stability problem for the switched model under constrained switching is considered and piecewise LKFs are adopted to obtain stability criteria. Since constrained switching is less conservative than arbitrary switching if the switching signal is known, one can know that the obtained results in this paper are less conservative than some existing ones. Two examples are given to illustrate the effectiveness of the obtained results.  相似文献   

15.
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   

16.
This paper presents novel approaches for stability analysis of switched linear time-delay stochastic systems under dwell time constraint. Instead of using comparison principle, piecewise switching-time-dependent discretized Lyapunov functions/functionals are introduced to analyze the stability of switched stochastic systems with constant or time-varying delays. These Lyapunov functions/functionals are decreasing during the dwell time and non-increasing at switching instants, which lead to two mode-dependent dwell-time-based delay-independent stability criteria for the switched systems without restricting the stability of the subsystems. Comparison and numerical examples are provided to show the efficiency of the proposed results.  相似文献   

17.
In this paper, the multiple model strategy is applied to the adaptive control of switched linear systems to improve the transient performance. The solvability of the adaptive stabilization problem of each subsystem is not required. Firstly, the two-layer switching mechanism is designed. The state-dependent switching law with dwell time constraint is designed in the outer-layer switching to guarantee the stability of the switched systems. During the interval of dwell time constraint, the parameter resetting adaptive laws are designed in the inner-layer switching to improve the transient performance. Secondly, the minimum dwell time constraint providing enough time for multiple model adaptive control strategy to work fully and maintaining the stability of the switched systems is found. Finally, the proposed switched multiple model adaptive control strategy guarantees that all the closed-loop system signals remain bounded and the state tracking error converges to zero.  相似文献   

18.
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   

19.
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   

20.
For the switched time-delay systems, the delay-dependent stability criteria will be derived under a state-driven switching law. A linear state transformation was introduced to transfer the switched time-delay system. On delay dependent stabilization analysis, we apply the Lyapunov-Krasovskii functionals to analyze the stabilization of the switched time-delay systems. This method can be applied to cases when all individual switched systems are unstable. Finally, one example is exploited to illustrate the proposed schemes.  相似文献   

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