On rational solution of the state equation of a finite automation (abstract only)

1987 ◽  
Author(s):  
R. Chaudhuri ◽  
H. Höft
Keyword(s):  
Rational Solution ◽  
State Equation ◽  
The State ◽  
Finite Automation

scholarly journals On rational solution of the state equation of a finite automaton

1988 ◽  
Vol 11 (2) ◽  
pp. 355-364
Author(s):  
R. Chaudhuri ◽  
H. Höft
Keyword(s):  
Finite Automaton ◽  
Rational Solution ◽  
State Equation ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

We prove that the necessary and sufficient condition for the state equation of a finite automatonMto have a rational solution is that the lexicographical Gödel numbers of the strings belonging to each of the end-sets ofMform an ultimately periodic set. A method of determining the existence of a rational solution of the state equation is also given.

scholarly journals Control Systems and Number Theory

2012 ◽  
Vol 2012 ◽  
pp. 1-28
Author(s):  
Fuhuo Li
Keyword(s):  
Zeta Functions ◽  
Feedback System ◽  
State Equation ◽  
The State ◽  
Point Of View ◽  
Pid Controllers ◽  
Primary Concern ◽  
Feedback Connection ◽  
Proper Understanding ◽  
Natural Way

We try to pave a smooth road to a proper understanding of control problems in terms of mathematical disciplines, and partially show how to number-theorize some practical problems. Our primary concern is linear systems from the point of view of our principle of visualization of the state, an interface between the past and the present. We view all the systems as embedded in the state equation, thus visualizing the state. Then we go on to treat the chain-scattering representation of the plant of Kimura 1997, which includes the feedback connection in a natural way, and we consider theH∞-control problem in this framework. We may view in particular the unit feedback system as accommodated in the chain-scattering representation, giving a better insight into the structure of the system. Its homographic transformation works as the action of the symplectic group on the Siegel upper half-space in the case of constant matrices. Both ofH∞- and PID-controllers are applied successfully in the EV control by J.-Y. Cao and B.-G. Cao 2006 and Cao et al. 2007, which we may unify in our framework. Finally, we mention some similarities between control theory and zeta-functions.

scholarly journals Disparity in Human Rights Violations: A Political and International Law Perspective

2016 ◽  
Vol 2 (3) ◽  
pp. 349
Author(s):  
Aidir Amin Daud
Keyword(s):  
Human Rights ◽  
International Law ◽  
Rational Solution ◽  
Double Series ◽  
Mass Murder ◽  
The State ◽  
Human Rights Violations ◽  
Natural Right ◽  
International Court ◽  
Political Interests

Right to life is non-derogable rights. A natural right that should not be revoked arbitrarily by anyone, including the state. A mass murder in events 1 October 1965 and Timor-Timor is a double series of states’ failure in protecting the rights of Indonesian peoples. Moreover, these two events get different treatment in its handling. The disparity in treatment between two cases is a big question related to the consistency of human rights enforcement in Indonesia. This study is a descriptive-qualitative research. While, to prove the truth, this study will use a comparative study. The findings show that the attitude of the United Nations that treat serious human rights violations in Timor-Timor and the events of 1965 in Indonesia, cannot be answered differently in the perspective of international law. Since it has a weakness where the political interests of ruling is very strong in influencing the decisions of the UN. The disparity in law enforcement in the event of serious human rights violations in 1965 and Timor-Timor due to the dynamics of international politics when it does not allow for the demands of human rights violations to the UNs’ International Court due to advantage for a certain state after the event. In order to reduce disparities in human rights violations, reconciliation is the most rational solution at this time compared remains demand the state for the violations. Besides, many human rights violations in certain countries that have successfully resolved through reconciliation approach.

Thermodynamic of the charged AdS black holes in Rastall gravity: P − V critical and Joule–Thomson expansion

2020 ◽  
Vol 35 (14) ◽  
pp. 2050113
Author(s):  
Sen Guo ◽  
Yan Han ◽  
Guo Ping Li
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Critical Temperature ◽  
Critical Exponents ◽  
State Equation ◽  
The State ◽  
Thermodynamic Quantities ◽  
Critical Temperatures ◽  
Ads Black Holes ◽  
And Inversion

In this paper, we study the thermodynamic of the charged AdS black holes in Rastall gravity. Firstly, the thermodynamic quantities of the charged AdS black holes in Rastall gravity are reviewed and the state equation of this black hole is obtained. Then, we investigate the [Formula: see text] critical and the Joule–Thomson expansion of the charged AdS black holes in Rastall gravity in which the critical temperature and the critical exponents are obtained. In addition, we get the inversion temperature and plot the isenthalpic and inversion curves in the [Formula: see text] plane, and also determine the cooling-heating regions of this black hole through the Joule–Thomson expansion. Finally, we investigate the ratio between the minimum inversion and critical temperatures, and find that the Rastall constant [Formula: see text] does not affect of this ratio.

scholarly journals Nonlinear dynamical behaviors of a moving membrane under external excitation

2018 ◽  
Vol 37 (4) ◽  
pp. 774-788
Author(s):  
Mingyue Shao ◽  
Jimei Wu ◽  
Yan Wang ◽  
Shudi Ying
Keyword(s):  
Nonlinear Vibration ◽  
Plate Theory ◽  
State Equation ◽  
Vibration Characteristics ◽  
The State ◽  
External Excitation ◽  
Nonlinear Dynamical ◽  
Runge Kutta Method ◽  
Time Histories ◽  
The Stability

In this paper, the nonlinear vibration characteristics of a moving printing membrane under external excitation are studied. Based on the Von Karman nonlinear plate theory, the nonlinear vibration equation of the axial motion membrane under the external excitation is deduced. The Galerkin’s method is used to discretize the vibration differential equations of the membrane, and then the state equation of the system is obtained. The state equation of the system is numerically solved by the fourth-order Runge–Kutta method. The relationship between the nonlinear vibration characteristics and the amplitude of external excitation, damping coefficient, and aspect ratio of the printing membrane is analyzed by using the time histories, phase-plane portraits, Poincare maps, and bifurcation diagrams. Chaotic intervals and the stable working range of the moving membrane are obtained. This study provides a theoretical basis for predicting and controlling the stability of the membrane.

Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders

2012 ◽  
Vol 60 (2) ◽  
pp. 279-284 ◽  
Author(s):  
M. Busłowicz
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
State Equation ◽  
The State ◽  
Natural Order ◽  
State Variables ◽  
The Stability ◽  
Derivatives Of ◽  
Fractional Orders ◽  
Time Linear

Abstract. The stability problem of continuous-time linear systems described by the state equation consisting of n subsystems with different fractional orders of derivatives of the state variables has been considered. The methods for asymptotic stability checking have been given. The method proposed in the general case is based on the Argument Principle and it is similar to the modified Mikhailov stability criterion known from the stability theory of natural order systems. The considerations are illustrated by numerical examples.

Formulation of a State Equation Including Fractional-Order State-Vectors

2007 ◽  
Author(s):  
Masaharu Kuroda
Keyword(s):  
Fractional Calculus ◽  
Control Theory ◽  
Fractional Order ◽  
State Equation ◽  
The State ◽  
Space Representation ◽  
Fractional Dynamics ◽  
Modern Control Theory ◽  
Order State ◽  
Modern Control

In recent years, applications of fractional calculus have flourished in various science and engineering fields. Particularly in engineering, control engineering appears to be expanding aggressively in its applications. Exemplary are the CRONE controller and the PIλDμ controller, which is categorizable into applications of fractional calculus in classical control theory. A state equation can be called the foundation of modern control theory. However, the relationship between fractional derivatives and the state equation has not been examined sufficiently. Consequently, a systematic procedure referred to by every researcher on the fractional-calculus side or control-theory side has not yet been established. For this study, therefore, involvement of fractional-order derivatives into a state equation is demonstrated here for ready comprehension by researchers. First, the procedures are explained generally; then the technique to incorporate the fractional-order state-vector into a conventional state equation is given as an example of the applications. The state-space representation in this study is useful not only for modeling a controlled system with fractional dynamics, but also for design and implementation of a controller to control fractional-order states. After we complete installation of the basic parts, we can apply the benefits of modern control theory, including robust control theories such as H-infinity and μ-analysis and synthesis in their integrities, to this fractional-order state-equation.

scholarly journals Research of the Robust Stability of Control Systems Using a New Approach to the Lyapunov Functions Construction

2015 ◽  
Vol 9 (11) ◽  
pp. 176 ◽  
Author(s):  
Gulzhan Uskenbayeva
Keyword(s):  
Robust Stability ◽  
Lyapunov Functions ◽  
Closed Loop ◽  
Time Derivative ◽  
State Equation ◽  
The State ◽  
New Approach ◽  
Vector Lyapunov Functions ◽  
The Matrix ◽  
The Right

<p class="22">We investigate a new approach to the construction of vector Lyapunov functions. An approach to the construction of Lyapunov functions as vector functions is developed based on a geometrical interpretation of the second method of Lyapunov. The negative of the gradient is determined from the components of the time derivative of the state vector (i.e., the right-hand side of the state equation). The region of stability of a closed-loop linear, stationary system with uncertain parameters is governed by inequalities in the matrix elements of the closed-loop system. This study developed a method for analysing the robust stability of SISO and MIMO linear systems in canonical forms.</p>

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