New approach on solving control problems with descriptor systems

Bunjaku, Drilon; Stefanovski, Jovan; Dimirovski, Georgi M.; Juričić, Đani

doi:10.1016/j.jfranklin.2018.11.037

Cited by 6 publications

(4 citation statements)

References 26 publications

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“…The state vectors x j (t) and the constant matrices A j , B j , and H j , (j = u, z, y), are of appropriate dimensions. The vectors u in (t) ∈ R m is the input of the filter (7), z o (t) ∈ R p is the output of the filter (8), and y o (t) ∈ R q is the output of the filter (9). The LPV descriptor system (4)-( 6) with the low pass filters ( 7)-( 9) can be written as ( 1)- (3), where…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

“…The problem of designing different types of controllers for different classes of descriptor systems has been considered by many researchers. Examples of these controllers are state‐feedback, 2,3 linear quadratic state‐feedback, 4

H_{\infty}

state‐feedback, 5

H_{2}

state‐feedback, 6 robust state‐feedback, 7 output‐feedback, 8,9 dynamic output‐feedback (DOF), 10

H_{\infty}

output‐feedback, 11

H_{\infty}

DOF, 12‐14

H_{2}

DOF, 15 mixed

H_{2}

H_{\infty}

DOF, 16 dissipative DOF, 17 observer based controller, 18 decentralized static output‐feedback, 19 adaptive controller, 20 Hamiltonian

H_{\infty}

controller, 21 neural network controller, 22 static‐output preview controller, 23 fuzzy controller, 24 sliding‐mode controller, 25 and model predictive controller 26 …”

Section: Introductionmentioning

confidence: 99%

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H∞ model following control of linear parameter‐varying descriptor systems

Abdullah

2022

Optim Control Appl Methods

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The topic of H ∞ model following control of linear parameter-varying (LPV) descriptor systems is considered in this article. The main objective of using the H ∞ model following control system is to ensure that the outputs of the LPV descriptor system track robustly the reference model outputs in the presence of bounded energy disturbances. The H ∞ model following control system consists of three subsystems: an LPV feedforward controller, an LPV reference model, and an LPV H ∞ descriptor dynamic output-feedback controller. The design matrices of these three subsystems are obtained by solving a set of tractable LPV matrix equations and inequalities. Two descriptor systems: an electrical circuit and a DC motor with an unbalanced disc are modeled as LPV descriptor systems and then used to show the design steps. The simulation results show the effectiveness of the proposed H ∞ model following control system.

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Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

H_{\infty}

state‐feedback, 5

H_{2}

state‐feedback, 6 robust state‐feedback, 7 output‐feedback, 8,9 dynamic output‐feedback (DOF), 10

H_{\infty}

output‐feedback, 11

H_{\infty}

DOF, 12‐14

H_{2}

DOF, 15 mixed

H_{2}

H_{\infty}

DOF, 16 dissipative DOF, 17 observer based controller, 18 decentralized static output‐feedback, 19 adaptive controller, 20 Hamiltonian

H_{\infty}

controller, 21 neural network controller, 22 static‐output preview controller, 23 fuzzy controller, 24 sliding‐mode controller, 25 and model predictive controller 26 …”

Section: Introductionmentioning

confidence: 99%

H∞ model following control of linear parameter‐varying descriptor systems

Abdullah

2022

Optim Control Appl Methods

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“…system with Differential-Algebraic Equations; (b) designing a nonlinear control. For, recently it was shown in [31] and [40], that the class of descriptor state-vector systems appears more advanced in describing the nature of physical systems than ordinary state-vector systems. It should be noted that, the descriptor system approach has been already applied successfully to aircraft control design [32] (see Example 7.2 in there).…”

Section: T mentioning

confidence: 99%

“…Remark 6. It is shown in [40] that in the case of linear descriptor system, using a preliminary feedback, we can obtain an impulse-free descriptor system, which is a property of a part of Assumption 2. Similar pre-feedback could be applied on the nonlinear descriptor system (18), (19).…”

Section: Feedback Stabilizability Of Nonlinear Descriptor Systemsmentioning

confidence: 99%

Stability of Nonlinear Descriptor Systems and Applications to Stabilization of Quadcopters

Bunjaku¹,

Stefanovski²,

Dimirovski³

2020

ACTA POLYTECH HUNG

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In this paper, new sufficient Lyapunov-like stability conditions and new Lyapunov-like, stabilizability conditions for nonlinear descriptor systems, with control, are presented along with their applications to quadcopter's flight stabilization. Most of these results are rather practical because they do not need solving nonlinear differential equations and nonlinear algebraic equations. Thus, the usage of these new results requires only the differentiation of functions. The numerical simulation results prove that the stabilization of the quadcopter is improved, in comparison with pure tracking control.

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