A Lyapunov-based small-gain theorem for interconnected switched systems

Yang, Guosong; Liberzon, Daniel

doi:10.1016/j.sysconle.2015.02.001

Cited by 57 publications

(41 citation statements)

References 29 publications

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“…Remark It should be pointed out that the main result in Theorem is more general than those existing results in the works of Dashkovskiy et al, Long and Zhao, and Yang and Liberzon, where all subsystems in switched systems are ISS or some are ISS. On the other hand, in classical ISS small‐gain theorem framework, the small‐gain condition does hold globally, which is a commonly used assumption in other works .…”

Section: Resultsmentioning

confidence: 81%

“…In contrast, condition implies that none of subsystems of the switched system is necessarily IOSS. Thus, condition is less restrictive than those in other works . As a matter of fact, the key feature of the condition is that

\sum_{l = 1}^{m} β_{k l} false(x false) false[V_{k} false(x false) - V_{l} false(x false) + μ_{k l} false(x false) false]

is the sum taken over all k ∈ M , which implies that

\frac{\partial V_{k}}{\partial x} f_{k} false(x, u false) \leq - γ V_{k} false(x false) + χ_{1} false(false‖ u false‖ false) + χ_{2} false(false‖ h_{k} false(x false) false‖ false)

is only required to be satisfied in a subregion Ω k .…”

Section: Resultsmentioning

confidence: 96%

“…Remark By using the average dwell time method, some sufficient conditions for the ISS and IOSS property of switched nonlinear systems were provided on the basis of the assumption that all subsystems in switched systems are ISS (IOSS) or some are ISS (IOSS) . In contrast, condition implies that none of subsystems of the switched system is necessarily IOSS.…”

Section: Resultsmentioning

confidence: 99%

“…First of all, new sufficient conditions for the IOSS property of switched nonlinear systems with non‐IOSS subsystems are provided. This is more general than those existing results where all subsystems in switched systems are ISS (IOSS) or some are ISS (IOSS) . Second, a state‐norm estimator for the switched system under study is designed explicitly.…”

Section: Introductionmentioning

confidence: 96%

“…On the other hand, when all or some subsystems are ISS, the ISS property of switched interconnected nonlinear systems has been studied recently based on small‐gain techniques . In addition, a small‐gain theorem for switched feedback interconnected systems with vector L 2 ‐gain was established in the work of Zhao and Hill, which, however, does not provide an approach to choosing switching signals.…”

Section: Introductionmentioning

confidence: 99%

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Input/output‐to‐state stability for switched nonlinear systems with unstable subsystems

Long

2019

Intl J Robust & Nonlinear

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Summary In this paper, a couple of sufficient conditions for input/output‐to‐state stability (IOSS) of switched nonlinear systems with non‐IOSS subsystems are derived by exploiting the multiple Lyapunov functions (MLFs) method. A state‐norm estimator–based small‐gain theorem is also established for switched interconnected nonlinear systems under some proper switching laws, where the small‐gain property of individual connected subsystems is not required in the whole state space instead only in some subregions of the state space. The state‐norm estimator for the switched system under study is explicitly designed via a constructive procedure by exploiting the MLFs method and the classical small‐gain technique. The presented results permit removal of a technical condition in existing literature, where all subsystems in switched systems are IOSS or some are IOSS. An illustrative example is also provided to illustrate the effectiveness of the theoretical results.

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Section: Resultsmentioning

confidence: 81%

\sum_{l = 1}^{m} β_{k l} false(x false) false[V_{k} false(x false) - V_{l} false(x false) + μ_{k l} false(x false) false]

is the sum taken over all k ∈ M , which implies that

\frac{\partial V_{k}}{\partial x} f_{k} false(x, u false) \leq - γ V_{k} false(x false) + χ_{1} false(false‖ u false‖ false) + χ_{2} false(false‖ h_{k} false(x false) false‖ false)

is only required to be satisfied in a subregion Ω k .…”

Section: Resultsmentioning

confidence: 96%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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Input/output‐to‐state stability for switched nonlinear systems with unstable subsystems

Long

2019

Intl J Robust & Nonlinear

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Exponential input‐to‐state stabilization of semilinear systems via intermittent control

Guo

Wang

Duan

et al. 2022

Intl J Robust & Nonlinear

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This paper is concerned with the exponential input‐to‐state stabilization of semilinear systems via aperiodically intermittent control and aperiodically intermittent sampled‐data control, respectively. The aperiodically intermittent control is characterized from the average sense. By designing an auxiliary timer to make a compromise between control activation intervals and control rest intervals and employing the piecewise Lyapunov function method, novel sufficient criteria are obtained to guarantee the exponential input‐to‐state stability of considered systems. As for the aperiodically intermittent sampled‐data control, the sampling instants can also be aperiodic. Especially, if the sampling instants are periodic, we employ a mixed piecewise Lyapunov functional method to obtain a relatively less conservative condition to guarantee the exponential input‐to‐state stability. Finally, a numerical example is presented to illustrate the effectiveness of the theoretical results.

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Distributed Control Synthesis Using Euler’s Method

Coënt¹,

Sandretto

Chapoutot

et al. 2017

Lecture Notes in Computer Science

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In a previous work, we explained how Euler's method for computing approximate solutions of systems of ordinary differential equations can be used to synthesize safety controllers for sampled switched systems. We continue here this line of research by showing how Euler's method can also be used for synthesizing safety controllers in a distributed manner. The global system is seen as an interconnection of two (or more) subsystems where, for each component, the sub-state corresponding to the other component is seen as an "input"; the method exploits (a variant of) the notions of incremental input-to-state stability (δ-ISS) and ISS Lyapunov function. We illustrate this distributed control synthesis method on a building ventilation example.

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A Lyapunov-based small-gain theorem for interconnected switched systems

Cited by 57 publications

References 29 publications

Input/output‐to‐state stability for switched nonlinear systems with unstable subsystems

Input/output‐to‐state stability for switched nonlinear systems with unstable subsystems

Exponential input‐to‐state stabilization of semilinear systems via intermittent control

Distributed Control Synthesis Using Euler’s Method

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