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Observer-based adaptive sliding mode fault-tolerant control for the underactuated space robot with joint actuator gain faults

Ronghua Lei, Li Chen (2021)

Kybernetika

An adaptive sliding mode fault-tolerant controller based on fault observer is proposed for the space robots with joint actuator gain faults. Firstly, the dynamic model of the underactuated space robot is deduced combining conservation law of linear momentum with Lagrange method. Then, the dynamic model of the manipulator joints is obtained by using the mathematical operation of the block matrices, hence the measurement of the angular acceleration of the base attitude can be omitted. Subsequently,...

On a geometrical study of population ecosystems.

Postolache, Mihai, Mocioalcă, Oana (1997)

Balkan Journal of Geometry and its Applications (BJGA)

On a “Liapunov like” function for an equation $\dot{z} = f (t, z)$ with a complex-valued function $f$

Josef Kalas (1982)

Archivum Mathematicum

On algebraic approach in quadratic systems.

Mencinger, Matej (2011)

International Journal of Mathematics and Mathematical Sciences

On eventual stability of impulsive systems of differential equations.

Soliman, A. A. (2001)

International Journal of Mathematics and Mathematical Sciences

On food chain in a chemostat with distinct removal rates.

El-Owaidy, Hassan M., Moniem, Ashraf A. (2003)

Applied Mathematics E-Notes [electronic only]

On $(h_{0}, h)$ -stability of autonomous systems.

Liu, Xinzhi (1992)

Journal of Applied Mathematics and Stochastic Analysis

On lopsided systems.

Javier Chavarriga, Nazim Salih (2002)

Extracta Mathematicae

On Lyapunov stability in hypoplasticity

Kovtunenko, Victor A., Krejčí, Pavel, Bauer, Erich, Siváková, Lenka, Zubkova, Anna V. (2017)

Proceedings of Equadiff 14

We investigate the Lyapunov stability implying asymptotic behavior of a nonlinear ODE system describing stress paths for a particular hypoplastic constitutive model of the Kolymbas type under proportional, arbitrarily large monotonic coaxial deformations. The attractive stress path is found analytically, and the asymptotic convergence to the attractor depending on the direction of proportional strain paths and material parameters of the model is proved rigorously with the help of a Lyapunov function....

On Lyapunov stability of linear systems of generalized ordinary differential equations.

Ashordia, M., Kekelia, N. (2000)

Memoirs on Differential Equations and Mathematical Physics

On Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point

Jiří Šremr (2025)

Applications of Mathematics

We discuss Lyapunov stability/instability of both lower and upper equilibria of free damped pendulum with periodically oscillating suspension point. We recall the results of Bogolyubov and Kapitza, provide new effective criteria of stability/instability of the equilibria of pendulum equation, and give the exact and complete proofs. The criteria obtained are formulated in terms of positivity/negativity of Green's functions of the periodic boundary value problems for linearized equations. Furthermore,...

On partial stability for delay systems

C. Corduneanu (1975)

Annales Polonici Mathematici

On practical stability and optimal stabilization of controlled motion

A. A. Martynyuk (1985)

Banach Center Publications

On properties of nonlinear second-order systems under nonlinear impulse perturbations.

Graef, John R., Karsai, János (1997)

Electronic Journal of Differential Equations (EJDE) [electronic only]

On small solutions of second order differential equations with random coefficients

László Hatvani, László Stachó (1998)

Archivum Mathematicum

We consider the equation $x^{''} + a^{2} (t) x = 0, a (t) : = a_{k} if t_{k - 1} \leq t < t_{k}, for k = 1, 2, ...,$ where ${a_{k}}$ is a given increasing sequence of positive numbers, and ${t_{k}}$ is chosen at random so that ${t_{k} - t_{k - 1}}$ are totally independent random variables uniformly distributed on interval $[0, 1]$ . We determine the probability of the event that all solutions of the equation tend to zero as $t \to \infty$ .