Observability of Nonlinear Control Systems on Time Scales - Sufficient Conditions

The Popov criterion for the stability of nonlinear control systems is considered. The Popov criterion gives sufficient conditions for stability of nonlinear systems in the frequency domain. It has a direct graphical interpretation and is convenient for both design and analysis. In the article presented, a table of transfer functions of linear parts of nonlinear systems is constructed. The tables includes frequency response functions and offers solutions to the stability of the given systems. The table makes a direct stability analysis of selected nonlinear systems possible. The stability analysis is solved analytically and graphically. Then it is easy to find out if the nonlinear system is or is not stable; the task that usually ranks among the difficult task in engineering practice.

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State feedback linearization of nonlinear control systems on homogeneous time scales

Nonlinear Analysis Hybrid Systems ◽

10.1016/j.nahs.2018.08.002 ◽

2019 ◽

Vol 31 ◽

pp. 69-85

Author(s):

Zbigniew Bartosiewicz ◽

Juri Belikov ◽

Ülle Kotta ◽

Małgorzata Wyrwas

Keyword(s):

Nonlinear Control ◽

Control Systems ◽

Time Scales ◽

Feedback Linearization ◽

State Feedback ◽

Nonlinear Control Systems

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External dynamical equivalence of time-varying nonlinear control systems on time scales

International Journal of Control ◽

10.1080/00207179.2011.584351 ◽

2011 ◽

Vol 84 (5) ◽

pp. 961-968 ◽

Cited By ~ 1

Author(s):

Z. Bartosiewicz ◽

E. Pawłuszewicz

Keyword(s):

Nonlinear Control ◽

Control Systems ◽

Time Scales ◽

Nonlinear Control Systems ◽

Time Varying ◽

Dynamical Equivalence

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On the Interval Stability of Weak-Nonlinear Control Systems with Aftereffect

The Scientific World JOURNAL ◽

10.1155/2016/6490826 ◽

2016 ◽

Vol 2016 ◽

pp. 1-8 ◽

Cited By ~ 5

Author(s):

Andriy Shatyrko ◽

Denys Khusainov

Keyword(s):

Differential Equations ◽

Nonlinear Control ◽

Control Systems ◽

Absolute Stability ◽

Neutral Type ◽

Sufficient Conditions ◽

Functional Method ◽

Nonlinear Control Systems ◽

Delay Argument ◽

Equations With Delay

Sufficient conditions of interval absolute stability of nonlinear control systems described in terms of systems of the ordinary differential equations with delay argument and also neutral type are obtained. The Lyapunov-Krasovskii functional method in the form of the sum of a quadratic component and integrals from nonlinearity is used at construction of statements.

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Robustness Analysis of a Type of Iterative Algorithm for R-L Fractional Nonlinear Control Systems in the Sense of L p Norm

Mathematical Problems in Engineering ◽

10.1155/2021/6661543 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

Yanfang Li ◽

Xianghu Liu ◽

Guangjun Xu

Keyword(s):

Nonlinear Control ◽

Control Systems ◽

Iterative Algorithm ◽

Mild Solutions ◽

Sufficient Conditions ◽

Robustness Analysis ◽

Nonlinear Control Systems ◽

Uncertain Disturbances ◽

The Laplace Transform ◽

Formula Type

The paper is concerned with the robustness analysis of a type of iterative algorithm for R-L fractional nonlinear control systems in the sense of L p norm. Firstly, according to the Laplace transform and M-L function, the concept of mild solutions of the system is derived. Secondly, we give the sufficient conditions of robustness analysis of the P D α -type ILC algorithm with uncertain disturbances and then study the robust analysis of the second-order P D α -type ILC algorithm. At last, two fractional examples are given to demonstrate the results.

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