Stability and Stabilizability Criteria for Discrete-Time Positive Switched Systems

Fornasini, Ettore; Valcher, Maria Elena

doi:10.1109/tac.2011.2173416

Cited by 191 publications

(105 citation statements)

References 35 publications

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“…In the case P ≥ 0, we provide an explicit and simplified characterization for internal positivity of system (17) that solely involves its dynamic matrices. …”

Section: Theorem 53 Systemmentioning

confidence: 99%

Positivity of discrete singular systems and their stability: An LP-based approach

Rami

Napp

2014

Automatica

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In this paper we present an efficient approach to the analysis of discrete positive singular systems. One of our main objectives is to investigate the problem of characterizing positivity of such systems. Previously, this issue was not completely addressed. We provide easily checkable necessary and sufficient conditions for such problem to be solved. On the other hand, we study the stability of discrete positive singular systems. Note that this is not a trivial problem since the set of admissible initial conditions is not the whole space but it is represented by a special cone. All the conditions we provide are necessary and sufficient, and are based on a reliable computational approach via linear programming.

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“…In the case P ≥ 0, we provide an explicit and simplified characterization for internal positivity of system (17) that solely involves its dynamic matrices. …”

Section: Theorem 53 Systemmentioning

confidence: 99%

Positivity of discrete singular systems and their stability: An LP-based approach

Rami

Napp

2014

Automatica

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“…There have been many available results about continuoustime positive switched systems [7][8][9][10][11] and discrete-time positive switched systems [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Guaranteed Cost Finite‐Time Control of Discrete‐Time Positive Impulsive Switched Systems

et al. 2018

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This paper considers the guaranteed cost finite-time boundedness of discrete-time positive impulsive switched systems. Firstly, the definition of guaranteed cost finite-time boundedness is introduced. By using the multiple linear copositive Lyapunov function (MLCLF) and average dwell time (ADT) approach, a state feedback controller is designed and sufficient conditions are obtained to guarantee that the corresponding closed-loop system is guaranteed cost finite-time boundedness (GCFTB). Such conditions can be solved by linear programming. Finally, a numerical example is provided to show the effectiveness of the proposed method.

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“…For arbitrary switching, common linear copositive Lyapunov function is applied in [17][18][19][20]. Some other results about switched positive linear systems can refer to literature [21][22][23][24][25][26]. The stability and robust stabilization issues by the multiple linear Lyapunov function approach is considered under the dwell time switching in [21,22].…”

Section: Introductionmentioning

confidence: 99%

“…The stability and robust stabilization issues by the multiple linear Lyapunov function approach is considered under the dwell time switching in [21,22]. The mutually relations among the linear copositive functions, quadratic copositive functions, and the quadratic positive definite functions are gives in [23]. For systems with exogenous disturbance, the L 1 -gain analysis and control synthesis are studied in [24,25].…”

Section: Introductionmentioning

confidence: 99%

State Feedback with Memory for Constrained Switched Positive Linear Systems

Liu

Zhang

2015

Entropy

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In this paper, the stabilization problem in switched linear systems with time-varying delay under constrained state and control is investigated. The synthesis of bounded state-feedback controllers with memory ensures that a closed-loop state is positive and stable. Firstly, synthesis with a sign-restricted (nonnegative and negative) control is considered for general switched systems; then, the stabilization issue under bounded controls including the asymmetrically bounded controls and states constraints are addressed. In addition, the results are extended to systems with interval and polytopic uncertainties. All the proposed conditions are solvable in term of linear programming. Numerical examples illustrate the applicability of the results.

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Stability and Stabilizability Criteria for Discrete-Time Positive Switched Systems

Cited by 191 publications

References 35 publications

Positivity of discrete singular systems and their stability: An LP-based approach

Positivity of discrete singular systems and their stability: An LP-based approach

Guaranteed Cost Finite‐Time Control of Discrete‐Time Positive Impulsive Switched Systems

State Feedback with Memory for Constrained Switched Positive Linear Systems

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