On guaranteed global exponential stability of polynomial singularly perturbed control systems

Bouzaouache, Hajer; Braïek, Naceur Benhadj

doi:10.1109/cesa.2006.4281667

Cited by 8 publications

(7 citation statements)

References 12 publications

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“…Among the main properties of this product presented in [29,[48][49][50], we recall the following useful ones…”

Section: Properties Of the Tensor Productmentioning

confidence: 99%

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Tensor Product‐Based Model Transformation and Optimal Controller Design for High Order Nonlinear Singularly Perturbed Systems

Bouzaouache

2019

Asian Journal of Control

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This paper investigates the optimization of a general class of nonlinear singularly perturbed systems. Tensor productbased modeling, algebraic properties, and singular perturbation theory played a significant role in the formulation of the derived reduced model. The obtained reduced output is a nonlinear state and input dependent vector. In this case, solving the optimal control problem when minimizing a quadratic performance index becomes more difficult because the weighting matrices vary as functions of states. So the reformulation of the initial problem is needed and the resolution is discussed from an analytical point of view. A two-step controller design procedure is suggested and an algorithm is proposed for the calculus of the gain matrices of the nonlinear control law. The Simulation results are presented to demonstrate the effectiveness of the approach and the power of the implemented algorithm.

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“…Among the main properties of this product presented in [29,[48][49][50], we recall the following useful ones…”

Section: Properties Of the Tensor Productmentioning

confidence: 99%

“…The constant matrices Ω, L i and r 1i can then be determined by matching the corresponding terms of (54) and (55). Finally, equation (48) yields 56) and the matrices Q 1i , Λ, T i can be calculated from (44), (45) and (56). (34) and B i (35) Given (36), one can write Φ(x)…”

Section: Determination Of the Matrices Q 1i (31-b) λ(32-b) And T I (mentioning

confidence: 99%

Tensor Product‐Based Model Transformation and Optimal Controller Design for High Order Nonlinear Singularly Perturbed Systems

Bouzaouache

2019

Asian Journal of Control

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“…Behavior of SPS for ǫ → 0 + Theorem 1 (compare with [27], Theorem 2.1). Under the assumptions (A1) and (A2) there exists ǫ 0 such that for every ǫ ∈ (0, ǫ 0 ] and for every input control u the SPS (5), (6) has in H(η) an unique realization, y ǫ , satisfying the inequality…”

Section: A1 For Limiting Problem (Inmentioning

confidence: 99%

“…We use the linear combination of the functions η(t), ζ ǫ (t) andζ ǫ (t) to approximate the exact solution of SPS (5), (6) by the following way. For η (t f )−η (t m ) ≤ 0 we define the approximate realizationỹ ǫ (t) of SPS (5), (6) bỹ…”

Section: Approximation Of Realization Of Spsmentioning

confidence: 99%

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On the approximation of the boundary layers for the controllability problem of nonlinear singularly perturbed systems

Vrabel

2012

Systems & Control Letters

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A new systematic approach to the construction of approximate solutions to a class of nonlinear singularly perturbed feedback control systems using the boundary layer functions especially with regard to the possible occurrence of the boundary layers is proposed. For example, problems with feedback control, such as the steady-states of the thermostats, where the controllers add or remove heat, depending upon the temperature registered in another place of the heated bar, can be interpreted with a second-order ordinary differential equation subject to a nonlocal three-point boundary condition. The O(ǫ) accurate approximation of behavior of these nonlinear systems in terms of the exponentially small boundary layer functions is given. At the end of this paper, we formulate the unsolved controllability problem for nonlinear systems.Recently in [27] we have shown that the solutions of (5), (6), in general, start with fast transient (|w ǫ (t i )| → ∞) of y ǫ (t) from y ǫ (t i ) to η(t), which is the so-called boundary layer phenomenon, and after decay of this transient they

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Decentralized observer based-Controller of Interconnected Analytical Nonlinear Systems Application for a Large Scale Power System

Abidi

Elloumi

2019

2019 International Conference on Advanced Systems and Emergent Technologies (IC_ASET)

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On guaranteed global exponential stability of polynomial singularly perturbed control systems

Cited by 8 publications

References 12 publications

Tensor Product‐Based Model Transformation and Optimal Controller Design for High Order Nonlinear Singularly Perturbed Systems

Tensor Product‐Based Model Transformation and Optimal Controller Design for High Order Nonlinear Singularly Perturbed Systems

On the approximation of the boundary layers for the controllability problem of nonlinear singularly perturbed systems

Decentralized observer based-Controller of Interconnected Analytical Nonlinear Systems Application for a Large Scale Power System

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