scholarly journals ABSOLUTE STABILITY OF A PROGRAM MANIFOLD OF NON-AUTONOMOUS BASIC CONTROL SYSTEMS

2018 ◽  
pp. 37-43
Author(s):  
Sailaubay Zhumatov
Keyword(s):  
Inverse Problem ◽  
Lyapunov Function ◽  
Control Systems ◽  
Absolute Stability ◽  
High Speed ◽  
Inverse Dynamics ◽  
Sufficient Conditions ◽  
System Of Differential Equations ◽  
Inverse Problems Of Dynamics ◽  
The Stability

In this paper the inverse dynamics problemisstudied: for a given manifold restore a force field, which lies in the tangent subspace to manifold. One of the general inverse problems of dynamics is solved: the corresponding system of differential equations is but as well as the stability is considered. This inverse problem is very important for a variety of mathematical models mechanics.Absolutestability of a program manifold of nonautonomous basic control systems with stationary nonlinearity is investigated.Theproblem of stability of the basic control systems is considered in the neighborhood of a program manifold. Nonlinearitysatisfies to conditions of local quadratic relations. The sufficient conditions of the absolute stability of the program manifold have been obtained relatively to a given vector-function by means of construction of Lyapunov function, in the form "quadratic form plus an integral from nonlinearity". The obtained results are used to solve the problem of the synthesis of high-speed regulators.

scholarly journals Iterative stability analysis for general polynomial control systems

2021 ◽  
Author(s):  
Bo Xiao ◽  
Hak-Keung Lam ◽  
Zhixiong Zhong
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Control Systems ◽  
Polynomial System ◽  
Stability Conditions ◽  
General Polynomial ◽  
Main Challenge ◽  
Detailed Simulation ◽  
Feasible Solutions ◽  
The Stability

AbstractThe main challenge of the stability analysis for general polynomial control systems is that non-convex terms exist in the stability conditions, which hinders solving the stability conditions numerically. Most approaches in the literature impose constraints on the Lyapunov function candidates or the non-convex related terms to circumvent this problem. Motivated by this difficulty, in this paper, we confront the non-convex problem directly and present an iterative stability analysis to address the long-standing problem in general polynomial control systems. Different from the existing methods, no constraints are imposed on the polynomial Lyapunov function candidates. Therefore, the limitations on the Lyapunov function candidate and non-convex terms are eliminated from the proposed analysis, which makes the proposed method more general than the state-of-the-art. In the proposed approach, the stability for the general polynomial model is analyzed and the original non-convex stability conditions are developed. To solve the non-convex stability conditions through the sum-of-squares programming, the iterative stability analysis is presented. The feasible solutions are verified by the original non-convex stability conditions to guarantee the asymptotic stability of the general polynomial system. The detailed simulation example is provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed approach is more capable to find feasible solutions for the general polynomial control systems when compared with the existing ones.

Lyapunov-Based Sufficient Conditions for Nonlinear Impulsive Systems

2011 ◽  
Vol 219-220 ◽  
pp. 508-512
Author(s):  
Yong Liang Gao ◽  
Xiao Wu Mu
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Lyapunov Function ◽  
Sufficient Conditions ◽  
Invariant Set ◽  
Positive Definite ◽  
Impulsive Systems ◽  
Stability Theorems ◽  
Sufficient Conditions For Convergence ◽  
The Stability

This paper focuses on the stability analysis and invariant set stability theorems for nonlinear impulsive systems. A set of Lyapunov-based sufficient conditions are established for these convergent properties. These results do not require the Lyapunov function to be positive definite. Inequalities relating the righthandside of the differential equation and the Lyapunov function derivative are involved for these results. These inequalities make it possible to deduce properties of the functions and thus leads to sufficient conditions for convergence and stability.

Robust Stability of Sequential Multi-input Multi-output Quantitative Feedback Theory Designs

2004 ◽  
Vol 127 (2) ◽  
pp. 250-256 ◽  
Author(s):  
Murray L. Kerr ◽  
Suhada Jayasuriya ◽  
Samuel F. Asokanthan
Keyword(s):  
Control Systems ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Internal Stability ◽  
Quantitative Feedback Theory ◽  
Recursive Design ◽  
Stability Theorems ◽  
Improved Design ◽  
The Stability ◽  
Necessary And Sufficient

This paper re-examines the stability of multi-input multi-output (MIMO) control systems designed using sequential MIMO quantitative feedback theory (QFT). In order to establish the results, recursive design equations for the SISO equivalent plants employed in a sequential MIMO QFT design are established. The equations apply to sequential MIMO QFT designs in both the direct plant domain, which employs the elements of plant in the design, and the inverse plant domain, which employs the elements of the plant inverse in the design. Stability theorems that employ necessary and sufficient conditions for robust closed-loop internal stability are developed for sequential MIMO QFT designs in both domains. The theorems and design equations facilitate less conservative designs and improved design transparency.

scholarly journals Global Mittag–Leffler Stabilization of Fractional-Order BAM Neural Networks with Linear State Feedback Controllers

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Hongyun Yan ◽  
Yuanhua Qiao ◽  
Lijuan Duan ◽  
Ling Zhang
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Fractional Order ◽  
State Feedback ◽  
Control Strategies ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Bam Neural Networks ◽  
Linear State ◽  
The Stability

In this paper, the global Mittag–Leffler stabilization of fractional-order BAM neural networks is investigated. First, a new lemma is proposed by using basic inequality to broaden the selection of Lyapunov function. Second, linear state feedback control strategies are designed to induce the stability of fractional-order BAM neural networks. Third, based on constructed Lyapunov function, generalized Gronwall-like inequality, and control strategies, several sufficient conditions for the global Mittag–Leffler stabilization of fractional-order BAM neural networks are established. Finally, a numerical simulation is given to demonstrate the effectiveness of our theoretical results.

scholarly journals On a program manifold’s stability of one contour automatic control systems

2017 ◽  
Vol 7 (1) ◽  
pp. 479-484 ◽  
Author(s):  
S. S. Zumatov
Keyword(s):  
Automatic Control ◽  
Control Systems ◽  
Absolute Stability ◽  
Sufficient Conditions ◽  
Automatic Control Systems ◽  
Lyapunov’S Second Method ◽  
Analysis Of Stability ◽  
The One ◽  
Controllable Systems ◽  
Control Feedback

AbstractMethodology of analysis of stability is expounded to the one contour systems automatic control feedback in the presence of non-linearities. The methodology is based on the use of the simplest mathematical models of the nonlinear controllable systems. Stability of program manifolds of one contour automatic control systems is investigated. The sufficient conditions of program manifold’s absolute stability of one contour automatic control systems are obtained. The Hurwitz’s angle of absolute stability was determined. The sufficient conditions of program manifold’s absolute stability of control systems by the course of plane in the mode of autopilot are obtained by means Lyapunov’s second method.

scholarly journals Lyapunov Characterization for the Stability of Stochastic Control Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Fakhreddin Abedi ◽  
Wah June Leong ◽  
Mohammad Abedi
Keyword(s):  
Control Systems ◽  
Stochastic Control ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Stability ◽  
Necessary And Sufficient

Lyapunov-like characterization for the problem of input-to-state stability in the probability of nonautonomous stochastic control systems is established. We extend the well-known Artstein-Sontag theorem to derive the necessary and sufficient conditions for the input-to-state stabilization of stochastic control systems. Illustrating example is provided.

scholarly journals Globally Exponential Stability of Impulsive Neural Networks with Given Convergence Rate

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Chengyan Liu ◽  
Xiaodi Li ◽  
Xilin Fu
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Convergence Rate ◽  
Exponential Stability ◽  
Stability Problem ◽  
Sufficient Conditions ◽  
Analysis Techniques ◽  
Globally Exponential Stability ◽  
The Stability

This paper deals with the stability problem for a class of impulsive neural networks. Some sufficient conditions which can guarantee the globally exponential stability of the addressed models with given convergence rate are derived by using Lyapunov function and impulsive analysis techniques. Finally, an example is given to show the effectiveness of the obtained results.

A New Approach to Popov Criterion for Stability Analysis of Nonlinear Control Systems

2012 ◽  
Vol 463-464 ◽  
pp. 1549-1552
Author(s):  
Ivan Svarc
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Nonlinear Control ◽  
Control Systems ◽  
Transfer Functions ◽  
Sufficient Conditions ◽  
Nonlinear Control Systems ◽  
Engineering Practice ◽  
The Stability ◽  
The Given

The Popov criterion for the stability of nonlinear control systems is considered. The Popov criterion gives sufficient conditions for stability of nonlinear systems in the frequency domain. It has a direct graphical interpretation and is convenient for both design and analysis. In the article presented, a table of transfer functions of linear parts of nonlinear systems is constructed. The tables includes frequency response functions and offers solutions to the stability of the given systems. The table makes a direct stability analysis of selected nonlinear systems possible. The stability analysis is solved analytically and graphically. Then it is easy to find out if the nonlinear system is or is not stable; the task that usually ranks among the difficult task in engineering practice.

ANALYSIS ON THE GLOBALLY EXPONENT SYNCHRONIZATION OF CHUA'S CIRCUIT USING ABSOLUTE STABILITY THEORY

2005 ◽  
Vol 15 (12) ◽  
pp. 3867-3881 ◽  
Author(s):  
XIAOXIN LIAO ◽  
PEI YU
Keyword(s):  
Control Systems ◽  
Stability Theory ◽  
Lyapunov Functions ◽  
Absolute Stability ◽  
Sufficient Conditions ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Theoretical Predictions ◽  
Simulation Results ◽  
Absolute Stability Theory

In this paper, the absolute stability theory and methodology for nonlinear control systems are employed to study the well-known Chua's circuit. New results are obtained for the globally exponent synchronization of two Chua's circuits. The explicit formulas can be easily applied in practice. With the aid of constructing Lyapunov functions, sufficient conditions are derived, under which two (drive-response) Chua's circuits are globally and exponentially synchronized, even if the motions of the systems are divergent to infinity. Numerical simulation results are given to illustrate the theoretical predictions.

scholarly journals On the Interval Stability of Weak-Nonlinear Control Systems with Aftereffect

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Andriy Shatyrko ◽  
Denys Khusainov
Keyword(s):  
Differential Equations ◽  
Nonlinear Control ◽  
Control Systems ◽  
Absolute Stability ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Nonlinear Control Systems ◽  
Delay Argument ◽  
Equations With Delay

Sufficient conditions of interval absolute stability of nonlinear control systems described in terms of systems of the ordinary differential equations with delay argument and also neutral type are obtained. The Lyapunov-Krasovskii functional method in the form of the sum of a quadratic component and integrals from nonlinearity is used at construction of statements.

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