On robust stability of switched systems in the context of Filippov solutions

Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafael

doi:10.1016/j.sysconle.2017.09.002

Cited by 9 publications

(5 citation statements)

References 38 publications

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“…[27] proposed the application of Filippov's method to the small‐signal analysis of the general DC‐DC converters, and [28] first attempted sets with large periodic input for the same. Nevertheless, from a mathematical perspective, further theoretical study of Filippov's methods is required [29]. Thus, there still exists some practical difficulties for equilibrium point control.…”

Section: Introductionmentioning

confidence: 99%

A practical stable control scheme under end point equivalence modulation for DC power supply converters

Lin

et al. 2021

IET Power Electronics

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A series of DC power supply converters can be described as linear affine systems with finite inputs and constrained switching frequency. In this study, a practical‐stability‐oriented general control framework with duty‐cycle‐like characteristics is deduced for such converters. First, a concept called End Point Equivalence Modulation (EPEM) is introduced to release constraints. Following this, a Control Lyapunov Function (CLF) is employed to design the switching law and the relationship between the boundary of the convergence zone and the switching frequency is derived. In addition, an optimized switching strategy is presented to halve the switching frequency without degrading the control performance, which is also helpful for reducing switching loss. Finally, a single‐phase inverter and buck converter are considered as case studies and analysis show that Sinusoidal Pulse Width Modulation (SPWM) and volt‐second balance guarantee their practical stability, respectively, which can be theoretically derived and proved under EPEM. All the proposed methods and controllers are validated both by simulations on MATLAB/Simulink and experiments in a rapid control prototype platform based on a FPGA module.

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Section: Introductionmentioning

confidence: 99%

A practical stable control scheme under end point equivalence modulation for DC power supply converters

Lin

et al. 2021

IET Power Electronics

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“…Briefly, SASs are represented by discontinuous right-hand side differential equations regarded as differential inclusion, in which a sliding mode may be occurring depending on the switching algorithm. It has been shown that the solutions to mentioned differential inclusion exist in the sense of Filippov, if the set-valued functions representing the differential inclusion are bounded, closed, convex, nonempty, and upper semicontinuous everywhere on the defined regions (Ahmadi et al, 2017). Continuous-time SASs have been studied from different aspects of control theory including both theoretical and practical cases.…”

Section: Introductionmentioning

confidence: 99%

Distributed min-projection control: A switching consensus protocol for switched affine multi-agent systems

Sinafar

Badamchizadeh

Kharrati

et al. 2020

Journal of Vibration and Control

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In this study, a distributed control problem is addressed for switched affine multi-agent systems. In dynamical systems with an affine control input, the use of error feedback is essential for the realization of consensus protocols, but different from most existing results with affine control multi-agent systems, switched affine multi-agent systems face additional difficulties in the analysis and control; meanwhile, affine diffusive coupling consensus algorithms are not applicable. For this reason, a switching signal is considered as a control mechanism. We study switched networks in which the leader’s state is accessible only for a portion of agents, and the Lyapunov matrix-based min-projection control strategy is proposed to determine the active mode for each agent based on the state information of the neighbors. Using parameter-dependent stability analysis, a range of different reference points can be tracked by distributed min-projection switching without any redesigning. Also, benefiting from the hybrid dynamical system, min-projection switch is modified such that a periodic time-triggered sampled control is introduced to obtain finite switching frequency. Finally, a multi-motor system fed by DC–DC buck–boost converters is simulated for a stepwise changing of leader signal and different dwell-time switching, and the effectiveness of proposed method is assessed.

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“…In general, switched linear systems (SLSs) are mainly composed of individual subsystems and the switched rules coordinating these subsystems. The structure properties of SLSs have been investigated by many researchers, and some efforts have been expended on controller design (Sun and Duan, 2019; Sun and Ge, 2005; Zhao and Hill, 2008; Zong et al, 2016) and stability analysis (Ahmadi et al, 2017; Baleghi and Shafiei, 2016; Kundu and Chatterjee, 2016; Sun and Wang, 2012; Zhang et al, 2015). For the identification of SLSs with Box and Jenkins models, there exist several crucial issues to be addressed, including mode detection (MD) and parameter identification (PI).…”

Section: Introductionmentioning

confidence: 99%

Identification of switched linear systems based on expectation-maximization and Bayesian algorithms

Chai

Wang

et al. 2020

Transactions of the Institute of Measurement and Control

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This study aims to determine how to deal with the identification from input and output data of switched linear systems (SLSs) with Box and Jenkins models. The identification difficulties of this system are that there exist unknown switched signal, unknown middle variables, and colored noise terms in the identification process. To address these issues, the proposed identification method proceeds in two stages, including the estimation of the switched signal of SLSs and the identification of the parameters of all subsystems. First, the Gaussian mixture model is established to represent the distribution of the input and output data of SLSs. Then, the posterior probability is calculated by the expectation-maximization (EM) algorithm and the naive Bayes classifier, and the switched signal is estimated according to the maximum probability criterion. Next, the auxiliary model based multi-innovation generalized extended least square (AM-MI-GELS) algorithm is used to estimate the parameters of all subsystems. Finally, the effectiveness of the proposed method is verified through the simulation example.

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On robust stability of switched systems in the context of Filippov solutions

Cited by 9 publications

References 38 publications

A practical stable control scheme under end point equivalence modulation for DC power supply converters

A practical stable control scheme under end point equivalence modulation for DC power supply converters

Distributed min-projection control: A switching consensus protocol for switched affine multi-agent systems

Identification of switched linear systems based on expectation-maximization and Bayesian algorithms

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