Vector fitting by pole relocation for the state equation approximation of nonrational transfer matrices

2000 ◽  
Vol 19 (6) ◽  
pp. 549-566 ◽  
Author(s):  
Adam Semlyen ◽  
Bj�rn Gustavsen
Keyword(s):  
State Equation ◽  
The State ◽  
Transfer Matrices ◽  
Vector Fitting

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.

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>

State estimation for stochastic polynomial systems with switching in the state equation

2017 ◽  
Vol 40 (9) ◽  
pp. 2732-2739
Author(s):  
Miguel Hernandez-Gonzalez ◽  
Michael V Basin
Keyword(s):  
Covariance Matrix ◽  
Polynomial System ◽  
Random Variable ◽  
Polynomial Systems ◽  
State Equation ◽  
The State ◽  
Nonlinear Functions ◽  
Degree Polynomial ◽  
Error Covariance ◽  
Finite Dimensional

The problem of designing a mean-square filter has been studied for stochastic polynomial systems, where the state equation switches between two different nonlinear functions, over linear observations. A switching signal depends on a random variable modelled as a Bernoulli distributed sequence that takes the quantities of zero and one. The differential equations for the state estimate and the error covariance matrix are obtained in a closed form by expressing the conditional expectation of polynomial terms as functions of the estimate and covariance matrix. Finite-dimensional filtering equations are obtained for a particular case of a third-degree polynomial system. Numerical simulations are carried out in two cases of switching between different linear and second degree polynomial functions.

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