By Tadeusz Kaczorek (auth.), Wojciech Mitkowski, Janusz Kacprzyk, Jerzy Baranowski (eds.)
This quantity offers a number of elements of non-integer order structures, often referred to as fractional platforms, that have lately attracted an expanding cognizance within the medical neighborhood of structures technological know-how, utilized arithmetic, keep watch over conception. Non-integer platforms became proper for plenty of fields of technological know-how and know-how exemplified by means of the modeling of sign transmission, electrical noise, dielectric polarization, warmth move, electrochemical reactions, thermal tactics, acoustics, and so forth. The content material is split into six components, each of which considers one of many at present appropriate difficulties. within the first half the belief challenge is mentioned, with a distinct specialize in optimistic structures. the second one half considers balance of sure periods of non-integer order structures with and with no delays. The 3rd half is concentrated on such vital elements as controllability, observability and optimization particularly in discrete time. The fourth half is concentrated on disbursed structures the place non-integer calculus results in new and engaging effects. the following half considers difficulties of suggestions and approximations of non-integer order equations and structures. the ultimate and so much broad half is dedicated to purposes. difficulties from mechatronics, biomedical engineering, robotics and others are all analyzed and solved with instruments from fractional platforms. This quantity got here to fruition because of excessive point of talks and fascinating discussions at RRNR 2013 - fifth convention on Non-integer Order Calculus and its purposes that happened at AGH collage of technological know-how and know-how in Kraków, Poland, which used to be equipped via the school of electric Engineering, Automatics, machine technological know-how and Biomedical Engineering.
Read or Download Advances in the Theory and Applications of Non-integer Order Systems: 5th Conference on Non-integer Order Calculus and Its Applications, Cracow, Poland PDF
Best theory books
This publication is dedicated to the mathematical research of types of financial dynamics and equilibria. those versions shape a huge a part of mathemati cal economics. types of financial dynamics describe the movement of an economic system via time. the elemental thought within the examine of those types is that of a trajectory, i.
This quantity includes the invited papers provided on the NATO complicated learn Workshop at the idea of Sunspots, held in Cambridge, England, 22-27 September 1991. the assumption of preserving this Workshop first arose through the sunlight Optical Telescope paintings store on Theoretical difficulties in High-Resolution sunlight Physics in Munich in 1985.
The two-volume set LNCS 8111 and LNCS 8112 represent the papers provided on the 14th overseas convention on computing device Aided structures concept, EUROCAST 2013, held in February 2013 in Las Palmas de Gran Canaria, Spain. the whole of 131 papers awarded have been conscientiously reviewed and chosen for inclusion within the books.
- Algebraic and Geometric Methods in Nonlinear Control Theory
- Theory and Practice of Geometric Modeling
- Extreme Value Theory and Applications: Proceedings of the Conference on Extreme Value Theory and Applications, Volume 1 Gaithersburg Maryland 1993
- Islamic Finance: Theory and Practice
- Flexible Polymer Chains in Elongational Flow: Theory and Experiment
Additional info for Advances in the Theory and Applications of Non-integer Order Systems: 5th Conference on Non-integer Order Calculus and Its Applications, Cracow, Poland
The fractional system (1) is called positive if and only if xk ∈ ℜ n+ and yk ∈ ℜ +p , k ∈ Z + for any initial conditions x0 ∈ ℜ n+ and all input sequences uk ∈ ℜ m + , k ∈ Z+ . Lemma 1.  If 0 < α < 1 then c j (α ) > 0 for j = 1,2,... Theorem 1.  The fractional (1) is positive for 0 < α < 1 if and only if Aα = A + αI n ∈ ℜ n+× n , B ∈ ℜ n+× m , C ∈ ℜ +p × n , D ∈ ℜ +p × m . (6) Remark 1. Note that the equation (4) describe a linear discrete-time system with increasing number of delays in state.
1000, at which we see that the trajectory is tending to the equilibrium point (0, 0). One can choose the function V (x1 , x2 ) = x21 + x22 that is positive deﬁnite and decrescent. 05 + n)) . Therefore by Theorem 1 the trivial solution of the considered system is stable. Stability of Fractional Diﬀerence Systems with Two Orders 5 51 Conclusions Using the Lyapunov direct method we studied the stability of the Caputo nonlinear fractional diﬀerence systems with two orders. We stated the suﬃcient conditions for uniform stability, uniformly asymptotic stability, and globally uniformly asymptotic stability for such systems.
Kybernetes: The International Journal of Systems & Cybernetics 38(7/8), 1059–1078 (2009) 11. : Realization problem for fractional continuous-time systems. Archives of Control Sciences 18(1), 43–58 (2008) 12. : Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs. Int. J. Appl. Math. Comp. Sci. 16(2), 101–106 (2006) 13. : Realization problem for positive discrete-time systems with delay. System Science 30(4), 117–130 (2004) 14. : Realization problem for positive fractional discrete-time linear systems.