Stability, $l_{2}$ -Gain, and Robust $H_{\infty }$ Control for Switched Systems via ${N}$ -Step-Ahead Lyapunov Function Approach

Xie, Yaen; Wen, Jiwei; Nguang, Sing Kiong

doi:10.1109/access.2017.2771455

Cited by 16 publications

(15 citation statements)

References 26 publications

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“…As mentioned in Xie et al (2017), the switching must be gentler when the monotonic requirements of LF are relaxed. The ADT guaranteeing GUAS for N = 1 , N = 2 , N = 3 and N = 4 can be solved as τ a 1 * = 6 . 5788 , τ a 2 * = 13 . 1576 , τ a 3 * = 19 . 7364 and τ a 4 * = 26 . 3153 , respectively.…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…Similar method was adopted to reduce conservatism in a class of non-homogenous Markovian jump systems by allowing LF to increase during the period of several sampling time step ahead of the current time within each jump mode (Wen et al, 2017). However, to our best knowledge, the exploration of non-monotonic results for ADT switched systems still remains open, especially when the N-step ahead scenario is taken into account (Xie et al, 2017). The essential difficulty is to construct an exponential damping law of the LF decreasing points, that is, to find the joint-point between the switching interval and the predictive horizon.…”

Section: Introductionmentioning

confidence: 99%

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Dissipative dynamic output feedback control for switched systems via multistep Lyapunov function approach

Xie

Liu

Luan

et al. 2019

Transactions of the Institute of Measurement and Control

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The conservatism reduction problem of dissipative dynamic output feedback (DOF) control for a class of average dwell time switched system is investigated via a multistep Lyapunov function (LF) approach. First, a larger dissipative region with guaranteed stability and specifically, smaller [Formula: see text] level can be achieved by increasing a predictive step N, which means the monotonic requirement of LF is relaxed. Then, based on the results of dissipative analysis, a robust dissipative DOF controller is further designed. Unlike the traditional method that introduces equality constraint to obtain numerical testable conditions with heuristic nature, a less conservative controller is designed, where the LF matrix is formulated without structural constraint.

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Section: Illustrative Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dissipative dynamic output feedback control for switched systems via multistep Lyapunov function approach

Xie

Liu

Luan

et al. 2019

Transactions of the Institute of Measurement and Control

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“…Stability analysis and synthesis, robust ∞ controller design, observer-based fuzzy controller design, and output feedback stabilization have been intensively studied. Some preliminary results for switched systems [38,39] and NMJSs [40] have also been reported.…”

Section: Introductionmentioning

confidence: 99%

Robust H∞ Filtering of Nonhomogeneous Markovian Jump Delay Systems via N-Step-Ahead Lyapunov-Krasovskii Functional Approach

Wen

Nguang

2019

Complexity

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In this paper, we study the robust H∞ filtering problem for a class of nonhomogeneous Markovian jump delay systems (NMJDSs) with an N-step-ahead Lyapunov-Krasovskii functional (NALKF) approach. The N-step-ahead approach is utilized to reduce the conservatism of robust H∞ filtering. We aim to design filters such that, for all possible time-varying transition probabilities and all admissible parameter uncertainties and time-delays, the filtering error system is mean-square stable with a smaller estimated error and a lower dissipative level. In terms of linear matrix inequalities, sufficient conditions for the solvability of the addressed problem are developed via a moving horizon method. An illustrative example is included to elucidate advantages of the developed results and the practical potential of NALKF approach for NMJDSs.

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“…The aforementioned paper [8] investigates an N -step ahead LF in the stability analysis and synthesis of a discrete-time switched system. Such an approach allows a non-monotonic behavior of LF both at the switching instants and during the running time of each subsystem but guarantees LF convergence to zero in the limit.…”

Section: Introductionmentioning

confidence: 99%

“…To this end, average dwell time switching logic has been utilized. Although the use of N -step ahead LF for stability analysis and synthesis of switching systems is interesting, not considering some points ends in inefficiency and improperness of theorems presented in [8].…”

Section: Introductionmentioning

confidence: 99%

Comments on “Stability, l₂-Gain, and Robust <inline-formula> <tex-math notation="LaTeX">$\text{H}_{\infty}$ </tex-math> </inline-formula> Control for Switched Systems via <italic>N</italic>-Step-Ahead Lyapunov Function Approach”

Farahani

Derakhshan

2019

IEEE Access

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This paper presents a momentous aspect that should be considered in the stability analysis and synthesis of switched systems by investigating an N-step ahead Lyapunov function (LF) approach. By considering these traits, the proposed incorrect theorems in the aforementioned paper are revised to new ones. An illustrative numerical example manifests the effectiveness of our proposed approach. Unlike the assertion in the aforementioned paper when the monotonic requirement of LF is relaxed, the switching is not necessarily gentler. Also, our results indicate that our approach guarantees lower average dwell time. INDEX TERMSSwitched system, average dwell time, N -step ahead Lyapunov function, robust control.

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Stability, $l_{2}$ -Gain, and Robust $H_{\infty }$ Control for Switched Systems via ${N}$ -Step-Ahead Lyapunov Function Approach

Cited by 16 publications

References 26 publications

Dissipative dynamic output feedback control for switched systems via multistep Lyapunov function approach

Dissipative dynamic output feedback control for switched systems via multistep Lyapunov function approach

Robust H∞ Filtering of Nonhomogeneous Markovian Jump Delay Systems via N-Step-Ahead Lyapunov-Krasovskii Functional Approach

Comments on “Stability, l₂-Gain, and Robust <inline-formula> <tex-math notation="LaTeX">$\text{H}_{\infty}$ </tex-math> </inline-formula> Control for Switched Systems via <italic>N</italic>-Step-Ahead Lyapunov Function Approach”

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Stability, $l_{2}$ -Gain, and Robust $H_{\infty }$ Control for Switched Systems via ${N}$ -Step-Ahead Lyapunov Function Approach

Cited by 16 publications

References 26 publications

Dissipative dynamic output feedback control for switched systems via multistep Lyapunov function approach

Dissipative dynamic output feedback control for switched systems via multistep Lyapunov function approach

Robust H∞ Filtering of Nonhomogeneous Markovian Jump Delay Systems via N-Step-Ahead Lyapunov-Krasovskii Functional Approach

Comments on “Stability, l2-Gain, and Robust <inline-formula> <tex-math notation="LaTeX">$\text{H}_{\infty}$ </tex-math> </inline-formula> Control for Switched Systems via <italic>N</italic>-Step-Ahead Lyapunov Function Approach”

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Comments on “Stability, l₂-Gain, and Robust <inline-formula> <tex-math notation="LaTeX">$\text{H}_{\infty}$ </tex-math> </inline-formula> Control for Switched Systems via <italic>N</italic>-Step-Ahead Lyapunov Function Approach”