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1.
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   

2.
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   

3.
The main objective of this paper is to present a non-predictive method in the design of nonlinear multi-input multi-output (MIMO) control systems with the presence of constraints that are determinant in practical conditions, namely, the frequency bandwidth limitation of the actuation system and saturation boundaries in control commands. If these constraints are applied in the non-predictive control design problem, it is not possible to simultaneously satisfy Lyapunov stability and actuation constraints, analytically. Instead of model-predictive-based algorithms, which in most cases are computationally expensive, this paper proposes an algorithm based on synthetic Lyapunov stability. In this technique, by defining an intelligent filter applied to the system desired trajectories, defining intelligent proximity coefficients in decoupled inequalities resulting from Lyapunov stability, and determining the admissible boundaries of control commands, a space of regulatory parameters is generated. By appropriately adjusting these parameters based on statistical analysis conducted on the overall dynamics of the system, the Lyapunov stability is guaranteed, and the mentioned control constraints are not violated. In summary, the proposed control algorithm includes the formulation of discrete-time dynamics of sliding functions, the presentation of the procedure of defining and adjusting the control algorithm parameters with the proposed synthetic stability criterion, and the calculation of control inputs based on constraints imposed on the problem. Finally, the algorithm is applied to a cart moving in the X-Y plane, including two rigid cooperative arms that are carrying a load. The most important features of synthetic Lyapunov stability compared to the model predictive-based method are its small computational load and its acceptable performance in satisfying both the Lyapunov stability conditions and determinant control constraints in more realistic situations.  相似文献   

4.
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   

5.
Stability notions and Lyapunov functions for sliding mode control systems   总被引：2，自引：0，他引：2  
The paper surveys mathematical tools required for stability and convergence analysis of modern sliding mode control systems. Elements of Filippov theory of differential equations with discontinuous right-hand sides and its recent extensions are discussed. Stability notions (from Lyapunov stability (1982) to fixed-time stability (2012)) are observed. Concepts of generalized derivatives and non-smooth Lyapunov functions are considered. The generalized Lyapunov theorems for stability analysis and convergence time estimation are presented and supported by examples from sliding mode control theory.  相似文献   

6.
A common approach to Lyapunov's stability control is to design a controller such that a Lyapunov function can be derived for the control system to ensure stability. This procedure often leads to a discontinuous controller. When the controller is implemented, the discontinuous terms are replaced with continuous functions to avoid chattering of the control signal. Two associated problems have been overlooked during this procedure. One is that discontinuous control systems are non-smooth, which violates the fundamental assumptions of solution theories and the applicability of Lyapunov's stability theory is questionable. Another problem is that the replacement of discontinuous terms may weaken stability, which can be critical. In this paper, we discuss proper stability analysis of discontinuous control systems using the extended Lyapunov's second method based on Filippov's solution concept for non-smooth systems. We further propose to utilize the concept of Lyapunov exponents to quantitatively analyze the stability of continuous control systems obtained by replacing the discontinuous terms in the discontinuous controllers. An example involving the stabilization of a two-link non-fixed-base robotic manipulator is presented for demonstration. This research fills the gap in designing continuous Lyapunov's stability controllers regarding limited available Lyapunov functions.  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.
In this paper, the exponential stability of a class of delayed neural networks described by nonlinear delay differential equations of the neutral type has been studied. By constructing appropriate Lyapunov functional and using the linear matrix inequality (LMI) optimization approach, a series of sufficient criteria is obtained ensuring the existence, uniqueness and global exponential stability of an equilibrium point of such a kind of delayed neural networks. These conditions are dependent on the size of the time delay and the measure of the space, which is usually less conservative than delay-independent and space-independent ones. And, these networks are generalized without assuming the boundedness and differentiability of the activate functions. The proposed LMI condition can be checked easily by recently developed algorithms. The results are new and improve the earlier work. Examples are provided to demonstrate the effectiveness and applicability of the proposed 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.
In this paper, the problem of stability analysis for linear systems with time-varying delays is considered. By the consideration of new augmented Lyapunov functionals, improved delay-dependent stability criteria for asymptotic stability of the system are proposed for two cases of conditions on time-varying delays with the framework of linear matrix inequalities (LMIs), which can be solved easily by various efficient convex optimization algorithms. The enhancement of the feasible region of the proposed criteria is shown via three numerical examples by the comparison of maximum delay bounds.  相似文献   

11.
The stability and stabilization conditions of the nonlinear system in Takagi–Sugeno's form are considered. The homogeneously polynomially nonquadratic (HPNQ) Lyapunov functions and homogeneously polynomially parameterized (HPP) state feedback laws are adopted. By generalizing the procedure based on the Polya's theorem, the asymptotically necessary and sufficient (ANS) stability and stabilization conditions in the case of HPNQ Lyapunov functions and HPP control laws are reformulated. The major contribution of this paper is to give the parallel results using the multiple indices, so that the slack matrices can be extensively utilized to improve the numerical efficiency. The effectiveness of the results is illustrated by the numerical examples.  相似文献   

12.
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   

13.
This paper investigates the problem of decentralized adaptive backstepping control for a class of large-scale stochastic nonlinear time-delay systems with asymmetric saturation actuators and output constraints. Firstly, the Gaussian error function is employed to represent a continuous differentiable asymmetric saturation nonlinearity, and barrier Lyapunov functions are designed to ensure that the output parameters are restricted. Secondly, the appropriate Lyapunov–Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions, and the neural networks are employed to approximate the unknown nonlinearities. At last, based on Lyapunov stability theory, a decentralized adaptive neural control method is proposed, and the designed controller decreases the number of learning parameters. It is shown that the designed controller can ensure that all the closed-loop signals are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of the origin. Two examples are provided to show the effectiveness of the proposed method.  相似文献   

14.
In this work a procedure for obtaining polytopic λ-contractive sets for Takagi–Sugeno fuzzy systems is presented, adapting well-known algorithms from literature on discrete-time linear difference inclusions (LDI) to multi-dimensional summations. As a complexity parameter increases, these sets tend to the maximal invariant set of the system when no information on the shape of the membership functions is available. λ-contractive sets are naturally associated to level sets of polyhedral Lyapunov functions proving a decay-rate of λ. The paper proves that the proposed algorithm obtains better results than a class of Lyapunov methods for the same complexity degree: if such a Lyapunov function exists, the proposed algorithm converges in a finite number of steps and proves a larger λ-contractive set.  相似文献   

15.
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16.
This paper deals with the problem of delay-dependent stability analysis for neural networks with time-varying delays. First, by constructing an augmented Lyapunov–Krasovskii functional and utilizing a generalized free-weighting matrix integral inequality, an improved stability criterion for the concerned network is derived in terms of linear matrix inequalities. Second, by considering a marginal augmented vector and modifying a Lyapunov–Krasovsii functional, a further enhanced stability criterion is presented. Third, a less conservative stability condition in which a relaxed inequality related to activation functions is added is introduced. Finally, three numerical examples are included to illustrate the advantage and validity of the proposed criteria.  相似文献   

17.
Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Since finite-time convergence implies nonuniqueness of system solutions in reverse time, such systems possess non-Lipschitzian dynamics. Sufficient conditions for finite-time stability have been developed in the literature using Hölder continuous Lyapunov functions. In this paper, we develop a general framework for finite-time stability analysis based on vector Lyapunov functions. Specifically, we construct a vector comparison system whose solution is finite-time stable and relate this finite-time stability property to the stability properties of a nonlinear dynamical system using a vector comparison principle. Furthermore, we design a universal decentralized finite-time stabilizer for large-scale dynamical systems that is robust against full modeling uncertainty. Finally, we present two numerical examples for finite-time stabilization involving a large-scale dynamical system and a combustion control system.  相似文献   

18.
This paper deals with systems that can switch their structure, including the differentiation order. It is shown that there are several non-equivalent cases for them, which all coincide when the derivation order is not switched but fixed at 1. For each of these cases, (asymptotic) stability results are obtained in this paper. This is accomplished by generalizing Common Lyapunov Functions (CLF) and Multiple Lyapunov Functions (MLF) methods, the latter when applied to fractional switching systems (FSS) in the resetting. Several examples are presented to illustrate that such Lyapunov functions exist for linear and nonlinear switched order systems. It is shown that the resetting fractional switching can be easily implemented by standard software. Finally, applications in adaptive integer-order problems are made by exploiting features of both fractional and integer-order systems.  相似文献   

19.
This paper aims at the problem of exponential stability for switched linear impulsive time-varying system. By constructing two different switched discretized Lyapunov functions, some new sufficient conditions ensuring the global exponential stability of switched linear impulsive time-varying system are provided, which can be employed to the case when all subsystems are unstable. Furthermore, we apply theoretical results to the consensus of multi-agent system with switching topologies. Finally, numerical examples demonstrate the effectiveness of given results.  相似文献   

20.
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   

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