Global Practical Stabilization of Discrete-Time Switched Affine Systems via a General Quadratic Lyapunov Function and a Decentralized Ellipsoid

Hejri, Mohammad

doi:10.1109/jas.2021.1004183

Cited by 6 publications

(8 citation statements)

References 34 publications

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“…smaller than [9] with an area of 28.23. The proposed techniques in [16], [17], [26] based on local optimizer tool PENBMI did not yield feasible solutions for this example with T s = 0.5. It is noted that in contrast to [9] and the present work, the solution procedure in [16], [17], [26] is not based on the gridding of scalar variables.…”

Section: Examplesmentioning

confidence: 89%

“…The proposed techniques in [16], [17], [26] based on local optimizer tool PENBMI did not yield feasible solutions for this example with T s = 0.5. It is noted that in contrast to [9] and the present work, the solution procedure in [16], [17], [26] is not based on the gridding of scalar variables. Instead, in these references, the BMI problems are treated directly as a nonlinear optimization problem, and as a result, they are more difficult to handle numerically.…”

Section: Examplesmentioning

confidence: 89%

“…The proof of this proposition is similar to the proof of Prop. 4 in [26] and is omitted for the brevity.…”

Section: σ(E(k)) = Arg Minmentioning

confidence: 99%

“…The approach in [16] was extended in [17] using switched centralized quadratic Lyapunov functions. Reference [26] extended the existing works [8], [10], [11], [17] employing single Lyapunov functions via a common shifted quadratic Lyapunov function and a shifted ellipsoid parameterized independently. These previous studies based on the common Lyapunov functions imply the existence of a Schur stable convex combination of the subsystems matrices as a necessary condition.…”

Section: Introductionmentioning

confidence: 99%

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Practical Stability Analysis and Switching Controller Synthesis for Discrete-time Switched Affine Systems via Linear Matrix Inequalities

Hejri

2022

Scientia Iranica

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This paper considers the practical asymptotic stabilization of a desired equilibrium point in discrete-time switched affine systems. The main purpose is to design a state feedback switching rule for the discrete-time switched affine systems whose parameters can be extracted with less computational complexities. In this regard, using switched Lyapunov functions, a new set of sufficient conditions based on matrix inequalities, are developed to solve the practical stabilization problem. For any size of the switched affine system, the derived matrix inequalities contain only one bilinear term as a multiplication of a positive scalar and a positive definite matrix. It is shown that the practical stabilization problem can be solved via a few convex optimization problems, including Linear Matrix Inequalities (LMIs) through gridding of a scalar variable interval between zero and one. The numerical experiments on an academic example and a DC-DC buck-boost converter, as well as comparative studies with the existing works, prove the satisfactory operation of the proposed method in achieving better performances and more tractable numerical solutions.

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Section: Examplesmentioning

confidence: 89%

Section: Examplesmentioning

confidence: 89%

“…The proof of this proposition is similar to the proof of Prop. 4 in [26] and is omitted for the brevity.…”

Section: σ(E(k)) = Arg Minmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Practical Stability Analysis and Switching Controller Synthesis for Discrete-time Switched Affine Systems via Linear Matrix Inequalities

Hejri

2022

Scientia Iranica

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“…Switched systems, as an important class of hybrid systems, can model many practical systems such as network systems [28], circuit systems [19], vehicle dynamics [18], etc. Therefore, the investigation on switched system has been paid much attention, the topic includes stabilization [14], filter design [2] and fault estimation [20], and so on. The observer based fault estimation method for switched systems has been concerned in the works herein, such as [11,34].…”

mentioning

confidence: 99%

Interval estimation methods of fault estimation for discrete-time switched systems

Huang¹,

Zhang²,

Chen³

et al. 2023

JIMO

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<p style='text-indent:20px;'>This paper investigates the fault estimation problem for discrete-time switched systems. Firstly, the sensor fault is regarded as an augmented state, and then the original system is converted into a singular system. After that, based on the obtained singular system, a robust augmented state observer is designed using <inline-formula><tex-math id="M1">\begin{document}$ L_{\infty} $\end{document}</tex-math></inline-formula> technique. Given above robust augmented state observer, an interval observer based on the zonotope method is established to complete the fault interval estimation. Finally, a circuit system is simulated to illustrate the efficiency of the proposed method.</p>

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A switching control strategy for policy selection in stochastic Dynamic Programming problems

Tipaldi,

Iervolino,

Massenio

et al. 2025

Automatica

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Global Practical Stabilization of Discrete-Time Switched Affine Systems via a General Quadratic Lyapunov Function and a Decentralized Ellipsoid

Cited by 6 publications

References 34 publications

Practical Stability Analysis and Switching Controller Synthesis for Discrete-time Switched Affine Systems via Linear Matrix Inequalities

Practical Stability Analysis and Switching Controller Synthesis for Discrete-time Switched Affine Systems via Linear Matrix Inequalities

Interval estimation methods of fault estimation for discrete-time switched systems

A switching control strategy for policy selection in stochastic Dynamic Programming problems

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