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1.
In this paper, the networked stabilization of discrete-time periodic piecewise linear systems under transmission package dropouts is investigated. The transmission package dropouts result in the loss of control input and the asynchronous switching between the subsystems and the associated controllers. Before studying the networked control, the sufficient conditions of exponential stability and stabilization of discrete-time periodic piecewise linear systems are proposed via the constructed dwell-time dependent Lyapunov function with time-varying Lyapunov matrix at first. Then to tackle the bounded time-varying packet dropouts issue of switching signal in the networked control, a continuous unified time-varying Lyapunov function is employed for both the synchronous and asynchronous subintervals of subsystems, the corresponding stabilization conditions are developed. The state-feedback stabilizing controller can be directly designed by solving linear matrix inequalities (LMIs) instead of iterative optimization used in continuous-time periodic piecewise linear systems. The effectiveness of the obtained theoretical results is illustrated by numerical examples.  相似文献   

2.
In this paper, the H∞ control problem of periodic piecewise systems with polynomial time-varying subsystems is addressed. Based on a periodic Lyapunov function with a continuous time-dependent Lyapunov matrix polynomial, the H∞ performance is studied. The result can be easily reduced to the conditions for periodic piecewise systems with constant subsystems or linear time-varying systems based on a common Lyapunov function or a linear time-varying Lyapunov matrix. Moreover, an H∞ controller with time-varying polynomial controller gain is proposed as well, which could be directly solved with the linear matrix inequalities. A numerical example is presented to demonstrate the effectiveness of the proposed method.  相似文献   

3.
This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for the finite-time stability are presented via a state transition matrix approach. Secondly, this paper also develops the Lyapunov function method to study the finite-time stability and stabilization of discrete time-varying stochastic systems based on matrix inequalities and linear matrix inequalities (LMIs) so as to Matlab LMI Toolbox can be used.The state transition matrix-based approach to study the finite-time stability of linear discrete time-varying stochastic systems is novel, and its advantage is that the state transition matrix can make full use of the system parameter informations, which can lead to less conservative results. We also use the Lyapunov function method to discuss the finite-time stability and stabilization, which is convenient to be used in practical computations. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results.  相似文献   

4.
This paper proposes new inequality-based functions to be Lyapunov functionals for the stability analysis of time-varying delay systems. The novel Lyapunov functionals are developed using a slack-matrices-based integral inequality for the first time. This is unlike most inequality-based functions that have been used as Lyapunov functionals which consist of single-matrices in their integral terms. Based on the new Lyapunov functionals, a new stability criterion is derived in the form of a matrix-valued quadratic function, which is proven to be negative definite using a geometry-based negativeness lemma. Two numerical examples showcase the effectiveness of our presented method.  相似文献   

5.
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   

6.
In this work, impulsive stabilization problems of discrete-time switched linear systems with time-varying delays are studied. The sequence of impulsive instants is nearly-periodic, i.e., it is close to a periodic impulse and the distance between them is an uncertain bounded term. A time-varying Lyapunov function is introduced to characterize the information of delays, switching signals and impulses, and a stability criterion LMI-based is obtained without any restrictions on the stability of the subsystems. Several design schemes of reduced-order/full-order impulsive controllers with or without time-varying delays are developed. Finally, three numerical examples are provided to illustrate the effectiveness of the established results.  相似文献   

7.
This paper is concerned with the stability analysis of time-varying delay systems. Unlike the construction of augmented Lyapunov functional and multiple integral Lyapunov functional, novel three Lyapunov functionals are suggested which are delay product type functions and lead to less conservative results. Based on newly developed Lyapunov functionals, three stability criteria are derived and their superiority is described by three numerical examples.  相似文献   

8.
This paper studies the stability analysis of linear systems with time-varying delay, which is supposed to be the trigonometric form. By utilizing the characteristics between time-varying delay and its derivative, a novel interval approximation method is proposed, which provides the new allowable delay sets. Then making use of Wirtinger inequality, reciprocally convex inequality and the looped Lyapunov–Krasovskii functionals, the stability criteria with less conservatism are obtained. Finally, two examples are used to show the effectiveness and efficiency of the stability criteria.  相似文献   

9.
In this paper, the problem of delay-dependent stability analysis of fractional-order systems with time-varying delay is investigated. First, a class of novel fractional-order integral inequalities for quadratic functions by constructing appropriate auxiliary functions is proposed, which has been proven to be useful in analyzing fractional-order systems with time-varying delay. Based on these proposed inequalities, the Lyapunov–Krasovskii functions are designed to deal with the time-varying delay terms, reducing the conservatism of the stability criteria. Furthermore, delay-dependent criteria are derived to achieve asymptotic stability of fractional-order systems with time-varying delay. Finally, two examples are provided to illustrate the effectiveness and feasibility of the proposed stability criteria.  相似文献   

10.
This paper deals with absolute stability of uncertain Lur’e systems with time-varying delay. By introducing a Lyapunov–Krasovskii functional related to a second-order Bessel–Legendre inequality, some absolute stability criteria are derived for the system under study. Different from some existing approaches, a remarkable feature of this paper is that the time-derivative of the Lyapunov–Krasovskii functional is estimated by a linear function rather than a quadratic function on the time-varying delay, thanks to the introduction of four extra vectors. As a result, the resulting absolute stability criteria are of less conservatism than some existing ones, which is demonstrated through three examples.  相似文献   

11.
This paper is concerned with robust stability analysis of second-order linear time-varying (SLTV) systems with time-varying uncertainties (perturbations). With the specific Lyapunov functions, a simple and neat algebraic criterion for testing uniformly asymptotic stability of SLTV systems are derived. Without transformation to a system of first-order equations, the new conditions are imposed directly on the time-varying coefficient matrices of the system. The main feature of the proposed algebraic criterion is that the uncertain coefficient matrices are time-varying and not necessarily symmetric. Finally, the proposed stability conditions are used to design the extending space structures system of the spacecraft. Simulation results are provided to illustrate the convenience and effectiveness of the proposed method.  相似文献   

12.
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   

13.
This paper investigates stability problems of a class of nonlinear impulsive switching systems with time-varying delays. Based on the common Lyapunov function method and Razumikhin technique, several stability criteria are established for nonlinear impulsive switching systems with time-varying delays. Our results show that switching systems can be stabilized by impulsive switching signals even if the system matrices are all unstable. In the absence of impulses, some of our results reduce to similar stability criteria for nonimpulsive switching systems in some recent research articles. Several examples with simulations are given to illustrate the efficiency of our results.  相似文献   

14.
This article proposes an approach to construct a Lyapunov function for a linear large-scale periodic system. In this case, in contrast to various variants of small-gain stability conditions for large-scale systems, the presence of the asymptotic stability property of independent subsystems is not assumed. To analyze the asymptotic stability of a large-scale system, the direct Lyapunov method is used in combination with the discretization method and identities of the commutator calculus. The main results are illustrated by means of examples.  相似文献   

15.
This paper is mainly focused on the stabilization problem of uncertain delayed periodic piecewise time-varying systems inclusive of disturbances and faults in actuators. More specifically, the considered system is encompassed of periodic dynamics, which exhibits the nature of switched systems with fixed switching sequence and dwell time. The control protocol is configured in the form of both the present and past state information of the addressed system with passive performance. Moreover, the proposed control approach discloses the stabilization issue mainly by resolving the effect of faults in actuator components. Precisely, the desired periodic gain matrices of the developed controller are calculated by way of solving some matrix inequalities which are derived by making use of Lyapunov stability theory and matrix polynomial approach. As a result, the asymptotic stability of the considered system is ensured in conjunction with satisfied disturbance attenuation index. Conclusively, the simulation results of two numerical examples including mass-spring damping system are presented for validating the theoretical result.  相似文献   

16.
This paper addresses the delay-dependent stability problem of linear systems with interval time-varying delays. A generalized free-matrix-based inequality is proposed and employed to derive stability conditions, which are less conservative than the Bessel–Legendre inequality. An augmented Lyapunov–Krasovskii functional is tailored for the generalized free-matrix-based inequality. Then, some items in the Lyapunov–Krasovskii functionals are integrated so as to relax its positive definite condition, which provides a more accurate lower bound for the Lyapunov–Krasovskii functionals. Therefore, some less conservative stability criteria are presented. Two numerical examples illustrate the effectiveness of the method.  相似文献   

17.
This article investigates the stability analysis for a class of continuous-time switched systems with state constraints under pre-specified dwell time switchings. The state variables of the studied system are constrained to a unit closed hypercube. Firstly, based on the definition of set coverage, the system state under saturation is confined to a convex polyhedron and the saturation problem is converted into convex hull. Then, sufficient conditions are derived by introducing a class of multiple time-varying Lyapunov functions in the framework of pre-specified dwell time switchings. Such a dwell time is an arbitrary pre-specified constant which is independent of any other parameters. In addition, the proposed Lyapunov functions can efficiently eliminate the “jump” phenomena of adjacent Lyapunov functions at switching instants. The feature of this paper is that the definition of set coverage is utilized to replace the restriction on the row diagonally dominant matrices with negative diagonal elements to analyze stability. The other feature of the constructed time-varying Lyapunov functions is that there are two time-varying functions. One of the two time-varying functions contains the jump rate, which will present a certain degree of freedom in designing the dwell time switching signal. An iterative linear matrix inequality (LMI) algorithm is presented to verify the sufficient conditions. Finally, two examples are presented to show the validity of the method.  相似文献   

18.
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   

19.
Abstract: In this paper, the bilateral teleoperation with haptic feedback is studied under the phase transition between the constraint and unconstraint motions. The stability of the teleoperation with both force feedback and phase transition is proven by Lyapunov–Krasovskii method and hybrid systems theory. The conditions of the theory results are more general than the others, they are time-varying delays, nonlinear systems, force feedback, and phase transition. By using the admittance control, the application results illustrate the efficiency of the proposed control method.  相似文献   

20.
This paper studies the consensus problem for a class of nonlinear multi-agent systems with asymmetric time-varying output constraints and completely unknown non-identical control directions. Firstly, in order to deal with the problem of asymmetric time-varying output constraints, the original output-constrained multi-agent systems are transformed into new unconstrained multi-agent systems by constructing the state transformation for each agent. Secondly, the emergence of multiple Nussbaum-type function terms is avoided by introducing novel sliding-mode-esque auxiliary variables and consensus estimate variables, which allows the control directions to be completely unknown non-identical. Thirdly, a novel control strategy is proposed by combining novel variables with state transformation method for the first time, which makes the design of distributed consensus protocol more concise. Through Lyapunov stability analysis, the proposed distributed protocol ensures that the output constraints are never violated and the consensus can be achieved asymptotically. Finally, a practical simulation example is given to demonstrate the effectiveness of the proposed distributed consensus protocol.  相似文献   

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