Discrete-Time Positive Periodic Systems With State and Control Constraints

Rami, Mustapha Ait; Napp, Diego

doi:10.1109/tac.2015.2438428

Cited by 30 publications

(6 citation statements)

References 38 publications

(35 reference statements)

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“…The equivalence of condition (iv) could be seen as an alternative way to revise the sufficient condition of Theorem 2.1 in Bougatef et al. [40] to a necessary and sufficient one, which has also been addressed in Remark 2.5 of Ait Rami and Napp [12]. By introducing a set of strictly positive vectors

v_{i}

, one can always guarantee the strictly positivity of the set of vectors

p_{i}^{'}

.…”

Section: Resultsmentioning

confidence: 99%

“…Different kinds of systems with positivity have been investigated, including Markov jump systems [6, 10, 11], periodic systems [12, 13], singular systems [14–16], switched systems [17–19], and time delay systems [20, 21]. For linear continuous time‐invariant positive systems, the stability,

L_{1}

‐, and

L_{\infty}

‐gain can be characterized by the linear inequality.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stability and stabilization of periodic piecewise positive systems: A time segmentation approach

Zhu

Lam

Song

et al. 2022

Asian Journal of Control

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This paper is concerned with the stability analysis and stabilization of periodic piecewise positive systems. By constructing a time‐scheduled copositive Lyapunov function with a time segmentation approach, an equivalent stability condition, determined via linear programming, for periodic piecewise positive systems is established. Based on the asymptotic stability condition, the spectral radius characterization of the state transition matrix is proposed. The relation between the spectral radius of the state transition matrix and the convergent rate of the system is also revealed. An iterative algorithm is developed to stabilize the system by decreasing the spectral radius of the state transition matrix. Finally, numerical examples are given to illustrate the results.

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v_{i}

, one can always guarantee the strictly positivity of the set of vectors

p_{i}^{'}

.…”

Section: Resultsmentioning

confidence: 99%

L_{1}

‐, and

L_{\infty}

‐gain can be characterized by the linear inequality.…”

Section: Introductionmentioning

confidence: 99%

Stability and stabilization of periodic piecewise positive systems: A time segmentation approach

Zhu

Lam

Song

et al. 2022

Asian Journal of Control

View full text Add to dashboard Cite

show abstract

“…According to Reference 32, the positivity and asymptotic stability conditions for discrete‐time periodic positive systems are given as follows.…”

Section: ℓ1‐ and ℓ∞‐Gain Analysis For Discrete‐time Systemsmentioning

confidence: 99%

“…For discrete‐time positive periodic systems, the reachability and controllability properties of positive periodic systems are studied by using the time‐lifted approach 30 and directed graph of the state matrices, 31 respectively. In Reference 32, the concept of periodic invariance with respect to a collection of boxes is introduced and applied to studying the stability and stabilization for discrete‐time positive periodic systems. For continuous‐time periodic piecewise positive systems, the diagonal quadratic Lyapunov function is used to characterize the exponential stability of the systems in Reference 33.…”

Section: Introductionmentioning

confidence: 99%

Input–output gain analysis of positive periodic systems

Zhu

Lam

Ebihara

2021

Intl J Robust & Nonlinear

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This paper investigates the input‐output gains, including ℓ1‐ and ℓ∞‐gains and L1‐ and L∞‐gains, of discrete‐time and continuous‐time positive periodic systems. For the discrete‐time case, the input–output gain can be characterized by linear inequalities. For the continuous‐time case, the input–output gain characterization problem turns into the existence problem of a positive periodic vector function. Based on some necessary and sufficient input–output gain conditions, we find the ℓ1‐ (L1‐) gain of discrete‐time (continuous‐time) positive periodic systems is equivalent to the of ℓ∞‐ (L∞‐) gain of the associated dual systems. Finally, two numerical examples are given to illustrate the results.

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“…The literature provided a unified controller design framework for positive systems. More results on positive systems can be referred to . With the progress of the study on positive systems, many classes of systems that are related to positive systems arise, one class of which is known as positive switched systems.…”

Section: Introductionmentioning

confidence: 99%

Improved Controller Design for Uncertain Positive Systems and its Extension to Uncertain Positive Switched Systems

Zhang

Zhao

Zhang

et al. 2017

Asian Journal of Control

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This paper is concerned with the controller design of uncertain positive systems. First, we decompose the feedback gain matrix K m×n into m × n non-negative components and m × n non-positive components. For the non-negative components, each component contains only one positive element and the other elements are zero. Similarly, each non-positive component contains only one negative element and the other ones are zero. Then, a simple and effective controller design approach of uncertain positive systems is proposed by incorporating the decomposed feedback gain matrix into the resulting closed-loop systems and further applied to uncertain positive switched systems. It is shown that the designed controller is less conservative compared with those in the literature. Finally, a numerical example is provided to verify the validity of the proposed design.

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Discrete-Time Positive Periodic Systems With State and Control Constraints

Cited by 30 publications

References 38 publications

Stability and stabilization of periodic piecewise positive systems: A time segmentation approach

Stability and stabilization of periodic piecewise positive systems: A time segmentation approach

Input–output gain analysis of positive periodic systems

Improved Controller Design for Uncertain Positive Systems and its Extension to Uncertain Positive Switched Systems

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