Page 1

Displaying 1 – 14 of 14

Showing per page

Fault tolerant control for uncertain time-delay systems based on sliding mode control

Jun Sheng Wu, Zhengxin Weng, Zuo Hua Tian, Song Jiao Shi (2008)

Kybernetika

Fault tolerant control for uncertain systems with time varying state-delay is studied in this paper. Based on sliding mode controller design, a fault tolerant control method is proposed. By means of the feasibility of some linear matrix inequalities (LMIs), delay dependent sufficient condition is derived for the existence of a linear sliding surface which guarantees quadratic stability of the reduced-order equivalent system restricted to the sliding surface. A reaching motion controller, which can...

Fine scales of decay of operator semigroups

Charles J. K. Batty, Ralph Chill, Yuri Tomilov (2016)

Journal of the European Mathematical Society

Motivated by potential applications to partial differential equations, we develop a theory of fine scales of decay rates for operator semigroups. The theory contains, unifies, and extends several notable results in the literature on decay of operator semigroups and yields a number of new ones. Its core is a new operator-theoretical method of deriving rates of decay combining ingredients from functional calculus and complex, real and harmonic analysis. It also leads to several results of independent...

Finite-time adaptive outer synchronization between two complex dynamical networks with nonidentical topological structures

Jie Wu, Yong-zheng Sun, Dong-hua Zhao (2015)

Kybernetika

In this paper, we investigate the finite-time adaptive outer synchronization between two complex dynamical networks with nonidentical topological structures. We propose new adaptive controllers, with which we can synchronize two complex dynamical networks within finite time. Sufficient conditions for the finite-time adaptive outer synchronization are derived based on the finite-time stability theory. Finally, numerical examples are examined to demonstrate the effectiveness and feasibility of the...

Floquetova teorie a stabilita lineárních diferenciálních rovnic druhého řádu s periodickými koeficienty

Jiří Šremr (2023)

Pokroky matematiky, fyziky a astronomie

Tento článek ukazuje možné použití Floquetovy teorie v otázce ljapunovské stability lineárních diferenciálních rovnic druhého řádu s periodickými koeficienty. Jsou uvedeny obecné věty o stabilitě řešení uvažovaných rovnic v řeči Floquetových multiplikátorů, které jsou následně využity v důkazech jednoduchých efektivních kritérií. Je také vysvětlena souvislost mezi Ljapunovovými a Floquetovými charakteristickými exponenty a ukázáno použití těchto pojmů mimo jiné v otázce stability rovnovážného stavu...

Fractional positive continuous-time linear systems and their reachability

Tadeusz Kaczorek (2008)

International Journal of Applied Mathematics and Computer Science

A new class of fractional linear continuous-time linear systems described by state equations is introduced. The solution to the state equations is derived using the Laplace transform. Necessary and sufficient conditions are established for the internal and external positivity of fractional systems. Sufficient conditions are given for the reachability of fractional positive systems.

Further higher monotonicity properties of Sturm-Liouville functions

Zuzana Došlá, Miloš Háčik, Martin E. Muldoon (1993)

Archivum Mathematicum

Suppose that the function q ( t ) in the differential equation (1) y ' ' + q ( t ) y = 0 is decreasing on ( b , ) where b 0 . We give conditions on q which ensure that (1) has a pair of solutions y 1 ( t ) , y 2 ( t ) such that the n -th derivative ( n 1 ) of the function p ( t ) = y 1 2 ( t ) + y 2 2 ( t ) has the sign ( - 1 ) n + 1 for sufficiently large t and that the higher differences of a sequence related to the zeros of solutions of (1) are ultimately regular in sign.

Further ultimate boundedness of solutions of some system of third order nonlinear ordinary differential equations

A. U. Afuwape, Mathew Omonigho Omeike (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper, we shall give sufficient conditions for the ultimate boundedness of solutions for some system of third order non-linear ordinary differential equations of the form X w i d t h 0 p t h e i g h t 5 . 46 p t t o 8 p t . . . + F ( X ¨ ) + G ( X ˙ ) + H ( X ) = P ( t , X , X ˙ , X ¨ ) where X , F ( X ¨ ) , G ( X ˙ ) , H ( X ) , P ( t , X , X ˙ , X ¨ ) are real n -vectors with F , G , H : n n and P : × n × n × n n continuous in their respective arguments. We do not necessarily require that F ( X ¨ ) , G ( X ˙ ) and H ( X ) are differentiable. Using the basic tools of a complete Lyapunov Function, earlier results are generalized.

Currently displaying 1 – 14 of 14

Page 1