Stability analysis for a class of switched positive nonlinear systems under dwell-time constraint

Tian, Dadong; Liu, Shutang

doi:10.1186/s13662-018-1547-5

Cited by 13 publications

(5 citation statements)

References 32 publications

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“…Choosing the multiple co-positive-type Lyapunov functional (24). Similar to the proof process of eorem 1, from (16), (17), and (39), we have…”

Section: Io-fts Performance Analysismentioning

confidence: 88%

“…Theorem 2. Consider the system (14), for given constants T f , λ p , p ∈ N, η, and a vector δ ≻ 0, if there exist positive vectors ] p ∈ R n , ρ p ∈ R n , 9 p ∈ R n , p ∈ N, such that (16), (17), (19), (20), and the following inequalities hold,…”

Section: Io-fts Performance Analysismentioning

confidence: 99%

“…ere are already some available results about positive switched nonlinear systems [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…Step 1. By adjusting the parameters λ p and solving(16),(17),(19),(20), (40)-(42), (52), and (53) via linear programming, positive vectors ] p , ρ p , 9 p , and Z p can be obtained (2). Step 2.…”

mentioning

confidence: 99%

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L₁ Input‐Output Finite‐Time Control of Positive Switched Nonlinear Systems

Liu

Cao

Fan

et al. 2019

Mathematical Problems in Engineering

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In this paper, the problem of L 1 input-output finite-time control of positive switched nonlinear systems with time-varying and distributed delays is investigated. Nonlinear functions considered in this paper are located in a sector field. Firstly, the proof of the positivity of switched positive nonlinear systems with time-varying and distributed delays is given, and the concept of L 1 inputoutput finite-time stability (L 1 IO-FTS) is firstly introduced. en, by constructing multiple co-positive-type nonlinear Lyapunov functions and using the average dwell time (ADT) approach, a state feedback controller is designed and sufficient conditions are derived to guarantee the corresponding closed-loop system is L 1 IO-FTS. Such conditions can be easily solved by linear programming. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

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“…Choosing the multiple co-positive-type Lyapunov functional (24). Similar to the proof process of eorem 1, from (16), (17), and (39), we have…”

Section: Io-fts Performance Analysismentioning

confidence: 88%

Section: Io-fts Performance Analysismentioning

confidence: 99%

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L₁ Input‐Output Finite‐Time Control of Positive Switched Nonlinear Systems

Liu

Cao

Fan

et al. 2019

Mathematical Problems in Engineering

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“…Especially, the switched systems whose individual all subsystems are positive are called positive switched systems. The stability and FTS issues are the main matter in the field of positive switched systems, which have been extensively investigated in the literature [14,16,25,38,40,42].…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Stability of Discrete Linear Singular Switched Positive Systems with Time-Delay by a Mode-Dependent Average Dwell Time Approach

Yimnet¹,

Niamsup²

2020

DSA

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The problem of positivity and finite-time stability for a class of discrete linear singular switched time-delay systems with mode-dependent average dwell time (MDADT) approach is investigated in this paper. New necessary and sufficient conditions for the positivity of the system are presented by employing the state-space singular value decomposition and monomial coordinate transformation methods. By establishing a novel copositive Lyapunov function and applying the MDADT switching strategy, some computable sufficient conditions are formulated to ensure the finite-time stability for a class of discrete linear singular switched positive time-delay systems in terms of algebraic linear matrix inequalities. Two numerical experiments are provided to illustrate the effectiveness and less conservativeness of the proposed results.

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Representations of general solutions to some classes of nonlinear difference equations

2019

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Stability analysis for a class of switched positive nonlinear systems under dwell-time constraint

Cited by 13 publications

References 32 publications

L₁ Input‐Output Finite‐Time Control of Positive Switched Nonlinear Systems

L₁ Input‐Output Finite‐Time Control of Positive Switched Nonlinear Systems

Finite-Time Stability of Discrete Linear Singular Switched Positive Systems with Time-Delay by a Mode-Dependent Average Dwell Time Approach

Representations of general solutions to some classes of nonlinear difference equations

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Stability analysis for a class of switched positive nonlinear systems under dwell-time constraint

Cited by 13 publications

References 32 publications

L1 Input‐Output Finite‐Time Control of Positive Switched Nonlinear Systems

L1 Input‐Output Finite‐Time Control of Positive Switched Nonlinear Systems

Finite-Time Stability of Discrete Linear Singular Switched Positive Systems with Time-Delay by a Mode-Dependent Average Dwell Time Approach

Representations of general solutions to some classes of nonlinear difference equations

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L₁ Input‐Output Finite‐Time Control of Positive Switched Nonlinear Systems

L₁ Input‐Output Finite‐Time Control of Positive Switched Nonlinear Systems