12 results
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2. Stability and $L_2$-Gain Analysis for Linear Time-Delay Systems With Delayed Impulses: An Augmentation-Based Switching Impulse Approach.
- Author
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Chen, Wu-Hua, Ruan, Zhen, and Zheng, Wei Xing
- Subjects
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LINEAR systems , *LINEAR matrix inequalities , *LINEAR statistical models , *EXPONENTIAL stability , *LYAPUNOV functions , *NEWTON-Raphson method - Abstract
In this paper, the stability and $L_2$ -gain properties of linear impulsive delay systems with delayed impulses are studied. Commonly employed techniques, in which the delayed impulses are treated using Newton–Leibniz formula, may not be applicable to $L_2$ -gain analysis, since they make the disturbance input appear in the impulse part. In order to circumvent the difficulty, we first augment the considered system to a time-delay system with switching nondelayed impulses. Due to the absence of delayed impulses, this new approach has advantages in constructing Lyapunov functions and handling the effects of impulse delays on the system performance. Switching-based time-dependent Lyapunov functions are introduced to deal with the resultant switching impulses of the augmented system. Sufficient conditions for exponential stability and $L_2$ -gain properties are derived in terms of linear matrix inequalities. Numerical examples are provided to illustrate the efficiency of the new approach. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
3. Input-to-State Stability of Time-Varying Switched Systems With Time Delays.
- Author
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Wu, Xiaotai, Tang, Yang, and Cao, Jinde
- Subjects
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TIME delay systems , *LYAPUNOV functions , *LINEAR matrix inequalities , *DIFFERENTIAL equations , *NUMERICAL analysis - Abstract
This paper considers the input-to-state stability (ISS) of time-varying switched systems with time delays, where the upper bound estimation for the operator of Lyapunov function (UBEOL) is assumed to be time varying and mode dependent. The ISS and integral ISS are investigated for time-varying switched systems with time delays by using the Lyapunov–Razumikhin and comparison theorem methods. Since the coefficient in the UBEOL is time varying and takes a positive/negative value, the subsystems consist of both ISS and non-ISS subsystems, simultaneously. It is shown that our presented results have wider applications than some existing works. Two examples, including one of the consensus for time-varying multiagent systems with cooperative and competitive protocols, are presented to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
4. Stability Analysis for Continuous-Time Switched Systems With Stochastic Switching Signals.
- Author
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Wu, Xiaotai, Tang, Yang, Cao, Jinde, and Mao, Xuerong
- Subjects
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STABILITY (Mechanics) , *SWITCHING systems (Telecommunication) , *STOCHASTIC systems , *CONTINUOUS time systems , *MARKOV processes - Abstract
This paper is concerned with the stability problem of randomly switched systems. By using the probability analysis method, the almost surely globally asymptotical stability and almost surely exponential stability are investigated for switched systems with semi-Markovian switching, Markovian switching, and renewal process switching signals, respectively. Two examples are presented to demonstrate the effectiveness of the proposed results, in which an example of consensus of multiagent systems with nonlinear dynamics is taken into account. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
5. Global Exponential/Finite-Time Stability of Nonlinear Adaptive Switching Systems With Applications in Controlling Systems With Unknown Control Direction.
- Author
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Chen, Weisheng, Wen, Changyun, and Wu, Jian
- Subjects
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NONLINEAR systems , *LYAPUNOV stability , *EXPONENTIAL stability , *ADAPTIVE control systems , *EIGENVALUES - Abstract
This paper focuses on the stability analysis and control of adaptive switching systems by establishing Lyapunov-based logic switching rules. Through considering performance-index-based adaptive switching control under a general framework, sufficient conditions are proposed and proved to ensure global generalized exponential stability and global finite-time stability. By taking these conditions as guidelines for designing control laws and logic switching rules, we explore their applications in controlling a class of lower-triangular nonlinear systems with an unknown control direction. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
6. Quasi-Time-Dependent Output Control for Discrete-Time Switched System With Mode-Dependent Average Dwell Time.
- Author
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Fei, Zhongyang, Shi, Shuang, Wang, Zhenhuan, and Wu, Ligang
- Subjects
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DISCRETE-time systems , *LYAPUNOV functions , *DIFFERENTIAL equations , *CHAOS generators , *FLIGHT control systems - Abstract
This paper is concerned with dynamic output feedback control for a class of switched systems with mode-dependent average dwell-time switching. By constructing a quasi-time-dependent Lyapunov function, the issues of global uniform asymptotic stability and $\ell _{2}$ -gain analysis for the switched system are addressed first. Then, a set of reduced-order output feedback controllers is designed, which is both mode-dependent and quasi-time-dependent. Compared with time-independent criteria, the new results greatly reduce the conservatism. The effectiveness and merits of the proposed method are illustrated with a numerical example. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
7. A Characterization of Integral ISS for Switched and Time-Varying Systems.
- Author
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Haimovich, H. and Mancilla-Aguilar, J. L.
- Subjects
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MATHEMATICAL models of time-varying systems , *STABILITY of nonlinear systems , *INTEGRAL theorems , *SWITCHING system performance , *SYSTEM dynamics ,PERSISTENCE - Abstract
Most of the existing characterizations of the integral input-to-state stability (iISS) property are not valid for time-varying or switched systems in cases where converse Lyapunov theorems for stability are not available. This paper provides a characterization that is valid for switched and time-varying systems, and shows that natural extensions of some of the existing characterizations result in only sufficient but not necessary conditions. The results provided also pinpoint suitable iISS gains and relate these to supply functions and bounds on the function defining the system dynamics. [ABSTRACT FROM PUBLISHER]
- Published
- 2018
- Full Text
- View/download PDF
8. Multiple Lyapunov Functions-Based Small-Gain Theorems for Switched Interconnected Nonlinear Systems.
- Author
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Long, Lijun
- Subjects
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LYAPUNOV functions , *NONLINEAR systems , *SMALL-gain theorem (Mathematics) , *STABILITY criterion , *DYNAMICAL systems - Abstract
Multiple Lyapunov functions (MLFs)-based small-gain theorems are presented for switched interconnected nonlinear systems with unstable subsystems, which extend the small-gain technique from its original non-switched nonlinear version to a switched nonlinear version. Each low dimensional subsystem does not necessarily have the input-to-state stability (ISS) property in the whole state space, and it only has individual ISS property in some subregions of the state space. The novelty of this paper is that integral-type MLFs and small-gain techniques are utilized to establish some MLFs-based small-gain theorems for switched interconnected nonlinear systems, which derive various stability results under some novel switching laws designed and construct integral-type MLFs. The small-gain theorems proposed cover several recent results as special cases, which also permit removal of a common restriction in which all low dimensional subsystems in switched interconnected systems are ISS or only some are ISS and others are not. Finally, two illustrative examples are presented to demonstrate the effectiveness of the results provided. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
9. Stability of Stochastic Nonlinear Systems With State-Dependent Switching.
- Author
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Wu, Zhaojing, Cui, Mingyue, Shi, Peng, and Karimi, Hamid Reza
- Subjects
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STOCHASTIC systems , *SYSTEM analysis , *DYNKIN diagrams , *LYAPUNOV stability , *QUASISTATIC processes - Abstract
In this paper, the problem of stability on stochastic systems with state-dependent switching is investigated. To analyze properties of the switched system by means of Itô's formula and Dynkin's formula, it is critical to show switching instants being stopping times. When the given active-region set can be replaced by its interior, the local solution of the switched system is constructed by defining a series of stopping times as switching instants, and the criteria on global existence and stability of solution are presented by Lyapunov approach. For the case where the active-region set can not be replaced by its interior, the switched systems do not necessarily have solutions, thereby quasi-solution to the underlying problem is constructed and the boundedness criterion is proposed. The significance of this paper is that all the results presented depend on some easily-verified assumptions that are as elegant as those in the deterministic case, and the proofs themselves provide design procedures for switching controls. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
10. Stability and Stabilizability of Continuous-Time Linear Compartmental Switched Systems.
- Author
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Valcher, Maria Elena and Zorzan, Irene
- Subjects
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STABILITY of linear systems , *SWITCHING theory , *ASYMPTOTIC distribution , *EXISTENCE theorems , *MATRICES (Mathematics) - Abstract
In this paper, we introduce continuous-time linear compartmental switched systems and investigate their stability and stabilizability properties. By their nature, these systems are always stable. Necessary and sufficient conditions for asymptotic stability for arbitrary switching functions, and sufficient conditions for asymptotic stability under certain dwell-time conditions on the switching functions are proposed. Finally, stabilizability is thoroughly investigated and proved to be equivalent to the existence of a Hurwitz convex combination of the subsystem matrices, a condition that, for positive switched systems, is only sufficient for stabilizability. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
11. Almost Sure Stability of Switching Markov Jump Linear Systems.
- Author
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Song, Yang, Yang, Jie, Yang, Taicheng, and Fei, Minrui
- Subjects
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JUMP processes , *STABILITY of linear systems , *SWITCHING theory , *STOCHASTIC approximation , *TRANSIENT analysis - Abstract
Recently a special hybrid system called Switching Markov Jump Linear System (SMJLS) is studied. A SMJLS is subject to a deterministic switching and a stochastic Markovain switching. To extend the results already obtained and to investigate some new aspects of such systems, our main contributions in this paper are: i) Transient analysis of Markov process, i.e., the expectations of the sojourn time, the activation number of any mode, and the number of switchings between any two modes and ii) two sufficient conditions of the exponential almost sure stability for a general SMJLS. Different from previous work, which is a special case of our study, the transition rate matrix for the random Markov process in our study is not fixed, but varies when a deterministic switching takes place. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
12. Stability and Stabilizability Criteria for Discrete-Time Positive Switched Systems.
- Author
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Fornasini, Ettore and Valcher, Maria Elena
- Subjects
- *
DISCRETE-time systems , *SWITCHING circuits , *LYAPUNOV functions , *ASYMPTOTIC expansions , *LINEAR systems , *QUADRATIC equations - Abstract
In this paper we consider the class of discrete-time switched systems switching between p autonomous positive subsystems. First, sufficient conditions for testing stability, based on the existence of special classes of common Lyapunov functions, are investigated, and these conditions are mutually related, thus proving that if a linear copositive common Lyapunov function can be found, then a quadratic positive definite common function can be found, too, and this latter, in turn, ensures the existence of a quadratic copositive common function. Secondly, stabilizability is introduced and characterized. It is shown that if these systems are stabilizable, they can be stabilized by means of a periodic switching sequence, which asymptotically drives to zero every positive initial state. Conditions for the existence of state-dependent stabilizing switching laws, based on the values of a copositive (linear/quadratic) Lyapunov function, are investigated and mutually related, too. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
- Full Text
- View/download PDF
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