On the synthesis of a polynomial controller for enlarging the stability domain for nonlinear discrete system

2020 ◽  
Vol 42 (10) ◽  
pp. 1834-1839 ◽  
Author(s):  
Bedoui Sabrine ◽  
Belhadj Brahim Anis ◽  
Elloumi Salwa ◽  
Benhadj Braiek Naceur
Keyword(s):  
Stability Region ◽  
Algebraic Method ◽  
Discrete Systems ◽  
Stability Domain ◽  
Attraction Domain ◽  
Initial Stability ◽  
Polynomial Controller ◽  
The Stability ◽  
Nonlinear Discrete System ◽  
Nonlinear Discrete Systems

This paper aims to propose an algebraic method for estimating the stability region for nonlinear discrete systems. The main contribution is the improvement of an existing technique to enlarge the initial stability region in which the asymptotic stability is guaranteed. To deal with the maximization issue, a state feedback controller is proposed to extend the largest estimation of attraction domain of nonlinear polynomial discrete systems. The proposed approach is illustrated and validated on an isothermal stirred tank reactor.

Generalization of a stability domain estimation method for nonlinear discrete systems

2016 ◽  
Vol 37 (2) ◽  
pp. 1130-1141 ◽  
Author(s):  
Rim Zakhama ◽  
Anis Bacha Bel Hadj Brahim ◽  
Naceur Benhadj Braiek
Keyword(s):  
Estimation Method ◽  
Discrete Systems ◽  
Stability Domain ◽  
Nonlinear Discrete Systems

scholarly journals Periodic Solutions with Prescribed Minimal Period for 2 n th-Order Nonlinear Discrete Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Haiping Shi ◽  
Peifang Luo ◽  
Zan Huang
Keyword(s):  
Periodic Solutions ◽  
Discrete System ◽  
Discrete Systems ◽  
Point Theory ◽  
Minimal Period ◽  
Main Approach ◽  
Nontrivial Periodic Solutions ◽  
Existence Of Periodic Solutions ◽  
Nonlinear Discrete System ◽  
Nonlinear Discrete Systems

In this paper, by using the critical point theory, some new results of the existence of at least two nontrivial periodic solutions with prescribed minimal period to a class of 2 n th-order nonlinear discrete system are obtained. The main approach used in our paper is variational technique and the linking theorem. The problem is to solve the existence of periodic solutions with prescribed minimal period of 2 n th-order discrete systems.

The influence of the Stokes and Archimedes forces on the stability of a two-phase flow

2003 ◽  
Vol 3 ◽  
pp. 266-270
Author(s):  
B.H. Khudjuyerov ◽  
I.A. Chuliev
Keyword(s):  
Spectral Method ◽  
Stability Region ◽  
Gas Flow ◽  
Two Phase Flow ◽  
Solid Phase ◽  
Stability Characteristic ◽  
Phase Flow ◽  
Two Phase ◽  
The Stability

The problem of the stability of a two-phase flow is considered. The solution of the stability equations is performed by the spectral method using polynomials of Chebyshev. A decrease in the stability region gas flow with the addition of particles of the solid phase. The analysis influence on the stability characteristic of Stokes and Archimedes forces.

Enlarging the region of stability in robust model predictive controller based on dual-mode control

2021 ◽  
pp. 014233122110123
Author(s):  
Fatemeh Khani ◽  
Mohammad Haeri
Keyword(s):  
Stability Region ◽  
Linear Matrix ◽  
Input State ◽  
Dual Mode ◽  
Model Predictive Controller ◽  
Mode Control ◽  
Robust Model ◽  
Output Constraints ◽  
Predictive Controller ◽  
The Stability

Industrial processes are inherently nonlinear with input, state, and output constraints. A proper control system should handle these challenging control problems over a large operating region. The robust model predictive controller (RMPC) could be an linear matrix inequality (LMI)-based method that estimates stability region of the closed-loop system as an ellipsoid. This presentation, however, restricts confident application of the controller on systems with large operating regions. In this paper, a dual-mode control strategy is employed to enlarge the stability region in first place and then, trajectory reversing method (TRM) is employed to approximate the stability region more accurately. Finally, the effectiveness of the proposed scheme is illustrated on a continuous stirred tank reactor (CSTR) process.

DRY TURBULENCE FROM A TIME-DELAYED CHUA'S CIRCUIT

1993 ◽  
Vol 03 (02) ◽  
pp. 645-668 ◽  
Author(s):  
A. N. SHARKOVSKY ◽  
YU. MAISTRENKO ◽  
PH. DEREGEL ◽  
L. O. CHUA
Keyword(s):  
Difference Equation ◽  
Stability Region ◽  
Nonlinear Difference Equation ◽  
Chua’S Circuit ◽  
Stability Boundaries ◽  
Chua's Circuit ◽  
Infinite Dimensional ◽  
Chaotic Region ◽  
The Stability ◽  
Left Portion

In this paper, we consider an infinite-dimensional extension of Chua's circuit (Fig. 1) obtained by replacing the left portion of the circuit composed of the capacitance C2 and the inductance L by a lossless transmission line as shown in Fig. 2. As we shall see, if the remaining capacitance C1 is equal to zero, the dynamics of this so-called time-delayed Chua's circuit can be reduced to that of a scalar nonlinear difference equation. After deriving the corresponding 1-D map, it will be possible to determine without any approximation the analytical equation of the stability boundaries of cycles of every period n. Since the stability region is nonempty for each n, this proves rigorously that the time-delayed Chua's circuit exhibits the "period-adding" phenomenon where every two consecutive cycles are separated by a chaotic region.

scholarly journals Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case

2010 ◽  
Vol 2010 ◽  
pp. 1-23 ◽  
Author(s):  
Josef Diblík ◽  
Denys Ya. Khusainov ◽  
Irina V. Grytsay ◽  
Zdenĕk Šmarda
Keyword(s):  
Lyapunov Functions ◽  
Critical Case ◽  
Autonomous Systems ◽  
Discrete Systems ◽  
Simple Eigenvalue ◽  
Discrete Equations ◽  
The Matrix ◽  
The Stability ◽  
Important Characterization

Many processes are mathematically simulated by systems of discrete equations with quadratic right-hand sides. Their stability is thought of as a very important characterization of the process. In this paper, the method of Lyapunov functions is used to derive classes of stable quadratic discrete autonomous systems in a critical case in the presence of a simple eigenvalueλ=1of the matrix of linear terms. In addition to the stability investigation, we also estimate stability domains.

Sign in / Sign up

Export Citation Format

Share Document