Sampled‐data state feedback stabilization of a class of nonlinear systems based on Euler approximation

Malik, Fahad Mumtaz; Malik, Mohammad Bilal; Munawar, Khalid

doi:10.1002/asjc.233

Cited by 18 publications

(25 citation statements)

References 19 publications

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“…where k i = k n a i , i = 1, … , n − 1, are constants dependent on q since C is dependent on q. By (7), (9), and (A6), we complete the proof.…”

Section: (A4)mentioning

confidence: 61%

“…Once q is fixed, by the definition of k i in (9), k i reduces to a constant. For i = 2, … , n − 1, i (·) are continuous functions of l i+1 , … , l n , and n (·) is a constant; thus, l i can be chosen such that…”

Section: Propositionmentioning

confidence: 99%

“…nonlinear plants is considered but only local or semiglobal stabilization can be guaranteed because the approximation errors are inevitable for nonlinear plants (see, for example, other works [5][6][7][8][9] and the references therein). The semiglobal stabilization in this context means that, as the sampling period tends to zero, the set of points from which convergence to an arbitrarily small ball is guaranteed to contain an arbitrarily large neighborhood of the origin.…”

Section: Introductionmentioning

confidence: 99%

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Output feedback stabilization for a general class of nonlinear systems via sampled‐data control

Zhao

2018

Intl J Robust & Nonlinear

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This paper considers global output feedback stabilization via sampled-data control for a general class of nonlinear systems, which admit unknown control coefficients and nonderivable output function. A sector region of the output function is given by utilizing a technical lemma, and a sampled-data controller is designed by combining a robust state stabilizer and a reduced-order sampled-data observer. By carefully choosing an appropriate sampling period, the proposed controller guarantees the globally asymptotical stability of the closed-loop systems. KEYWORDSnonlinear systems, output feedback, sampled-data control, unknown output function where (t) = ( 1 (t), … , n (t)) ⊤ ∈ R n is the unmeasurable state, u(t) ∈ R is the control input, and y(t) ∈ R is the output. 1 (t), … , n (t) are unknown control coefficients, and h(·) is an unknown output function. For i = 1, … , n, nonlinearities f i (·) are assumed to be continuous in t and locally Lipschitz in and u, and f i (t, 0, 0) = 0. Output function h(·) is Lipschitz in its argument and vanishes at zero.With the rapid development of computer technology, more and more controllers are being implemented by digital computers. The design and analysis of sampled-data control for nonlinear systems have received a great deal of attention (see, for example, other works 1-4 ). However, it is not a trivial problem to design sampled-data controllers for nonlinear systems because unlike the linear case, the equivalence between sampled linear continuous-time systems and discrete-time systems is no longer available. In the literatures, a discretization method based on the discrete-time approximation of Int J Robust Nonlinear Control. 2018;28:2853-2867.wileyonlinelibrary.com/journal/rnc

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“…where k i = k n a i , i = 1, … , n − 1, are constants dependent on q since C is dependent on q. By (7), (9), and (A6), we complete the proof.…”

Section: (A4)mentioning

confidence: 61%

Section: Propositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Output feedback stabilization for a general class of nonlinear systems via sampled‐data control

Zhao

2018

Intl J Robust & Nonlinear

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“…In what follows, we will estimate the items in the right-hand side of (15). First by the definition of ′ i s, using Lemma II.1, we have…”

Section: Withmentioning

confidence: 99%

Global Robust Stabilization via Sampled‐Data Output Feedback for Nonlinear Systems with Uncertain Measurement and Control Gains

Zhang¹,

Qian²,

Li³

et al. 2014

Asian Journal of Control

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This paper studies the problem of using a sampled-data output feedback controller to globally stabilize a class of nonlinear systems with uncertain measurement and control gains. A reduced-order observer and a linear output control law, both in the sampled-data form, are designed without the precise knowledge of the measurement and control gains except for their bounds. The observer gains are chosen recursively in a delicate manner by utilizing the output feedback domination approach. The allowable sampling period is determined by estimating and restraining the growth of the system states under a zero-order-hold input with the help of the Gronwall-Bellman Inequality. A DC-DC buck power converter as a real-life example will be shown by numerical simulations to demonstrate the effectiveness of the proposed control method.

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“…Such systems function in the stochastic environment. High standards of quality of the modern control systems requires considering internal and external random disturbances, and the effect of delay of the Object of control, during their design and integration .…”

Section: Introductionmentioning

confidence: 99%

Dynamic Pulse‐Frequency Modulation in Objects Control with Delay

Aitchanov

Kurmanov

Umarov

2011

Asian Journal of Control

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This paper describes the development of the method of building mathematical models of dynamic pulse-frequency systems of automatic control of objects with random parameters and delay in the class of stochastic functional series of Voltaire and differential equations of Ito. In order to obtain mathematical descriptions of the system we have used homogenous models equivalent and majorizing processes in which are identical with the processes of the real stochastic dynamic pulse-frequency system of control of objects with delay. Obtained mathematical models of stochastic dynamic pulse-frequency systems of automatic control of objects with delay in the class of functional series of Voltaire and differential equations of Ito represent a further development of methods of description of "input-output" systems and "state space" and serve as a basis for developing methods of analysis and synthesis of the given class of automatic control systems.

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Sampled‐data state feedback stabilization of a class of nonlinear systems based on Euler approximation

Cited by 18 publications

References 19 publications

Output feedback stabilization for a general class of nonlinear systems via sampled‐data control

Output feedback stabilization for a general class of nonlinear systems via sampled‐data control

Global Robust Stabilization via Sampled‐Data Output Feedback for Nonlinear Systems with Uncertain Measurement and Control Gains

Dynamic Pulse‐Frequency Modulation in Objects Control with Delay

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