Stability and stabilization of positive switched systems with mode-dependent average dwell time

Zhang, J.; Han, Zhengzhi; Zhu, Fuliang; Huang, Jun

doi:10.1016/j.nahs.2013.01.005

Cited by 125 publications

(83 citation statements)

References 21 publications

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“…Then by Lemma 2.3, the trajectory of the system satisfies 0 ≼ x(k) ≼ d for any initial condition 0 ≼ x(0) ≼ d. Using this fact together with inequality (17), it is easy to see that the controllers u(k) = G p x(k) satisfy 0 ≼ u(k) ≼ G p d ≼ū. This completes the proof.…”

Section: Bounded and Sign-restricted Controlsmentioning

confidence: 83%

Controller synthesis for constrained discrete-time switched positive linear systems

Liu

Zhang

Pang

et al. 2016

Nonlinear Analysis: Hybrid Systems

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Section: Bounded and Sign-restricted Controlsmentioning

confidence: 83%

Controller synthesis for constrained discrete-time switched positive linear systems

Liu

Zhang

Pang

et al. 2016

Nonlinear Analysis: Hybrid Systems

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“…We skip the comparison of the obtained average dwell time computation with other methods in the literature since they either require a specified convergence rate as in [33] or they refer to in mode-dependent form as in [34], namely for each subsystem a certain average dwell time condition is imposed. Example 1.…”

Section: Illustrative Examplesmentioning

confidence: 99%

Graph‐Based Dwell Time Computation Methods for Discrete‐Time Switched Linear Systems

Ilhan

Karabacak

2016

Asian Journal of Control

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Analytical computation methods are proposed for evaluating the minimum dwell time and the average dwell time guaranteeing the asymptotic stability of a discrete-time switched linear system whose switchings are assumed to respect a given directed graph. The minimum and average dwell time can be found using the graph that governs the switchings, and the associated weights. This approach, which is used in a previous work for continuous-time systems having non-defective subsystems, has been adapted to discrete-time switched systems and generalized to allow defective subsystems. Moreover, we present a novel method to improve the dwell time estimation in the case of bimodal switched systems. In this method, scaling algorithms to minimize the condition number have been used to give better minimum dwell time and average dwell time estimates.

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“…Actually, the study of positive switched systems is more challenging than that of general switched systems because the features of positive systems and the features of switched systems have to be combined to obtain elegant results [20]. It should be pointed out that many previous results on positive switched systems focus mainly on stability analysis and controller synthesis [21][22][23][24][25][26][27][28][29], such as exponential stability [21][22][23][24][25], asymptotic stability [26], finite time stability (FTS) [27,28], and input-output finite time stability (IO-FTS) [30].…”

Section: Introductionmentioning

confidence: 99%

Input–Output Finite Time Stabilization of Time-Varying Impulsive Positive Hybrid Systems under MDADT

Yao

2017

Applied Sciences

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Time-varying impulsive positive hybrid systems based on finite state machines (FSMs) are considered in this paper, and the concept of input-output finite time stability (IO-FTS) is extended for this type of hybrid system. The IO-FTS analysis of the single linear time-varying system is given first. Then, the sufficient conditions of IO-FTS for hybrid systems are proposed via the mode-dependent average dwell time (MDADT) technique. Moreover, the output feedback controller which can stabilize the non-autonomous hybrid systems is derived, and the obtained results are presented in a linear programming form. Finally, a numerical example is provided to show the theoretical results.

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Stability and stabilization of positive switched systems with mode-dependent average dwell time

Cited by 125 publications

References 21 publications

Controller synthesis for constrained discrete-time switched positive linear systems

Controller synthesis for constrained discrete-time switched positive linear systems

Graph‐Based Dwell Time Computation Methods for Discrete‐Time Switched Linear Systems

Input–Output Finite Time Stabilization of Time-Varying Impulsive Positive Hybrid Systems under MDADT

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