Control Systems. Stabilization of Linear Systems

1997 ◽  
pp. 171-197
Author(s):  
Aristide Halanay ◽  
Judita Samuel
Keyword(s):  
Control Systems ◽  
Linear Systems

scholarly journals On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sendren Sheng-Dong Xu ◽  
Chih-Chiang Chen
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Switched Systems ◽  
The Other ◽  
Linear Control ◽  
Linear Control Systems ◽  
Problem Statement ◽  
Theoretical Derivation ◽  
Control Laws ◽  
Numerical Examples

The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence of two conditions regarding the existence of stabilizing switching laws between two unstable linear systems. One is effective for theoretical derivation, while the other is implementable, and a class of stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is then proposed. Then, the study is further extended to the issue concerning the construction of quadratically stabilizing switching laws among unstable linear systems and unstabilizable linear control systems. The obtained results are employed to study the existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable linear control systems. The numerical examples are illustrated and simulated to show the feasibility and effectiveness of the proposed methods.

scholarly journals Manifold Calculus in System Theory and Control—Fundamentals and First-Order Systems

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2092
Author(s):  
Simone Fiori
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Linear Control Systems ◽  
First Order ◽  
Curved Manifolds ◽  
Non Linear ◽  
Covariant Derivation ◽  
Non Linear Systems ◽  
And Control

The aim of the present tutorial paper is to recall notions from manifold calculus and to illustrate how these tools prove useful in describing system-theoretic properties. Special emphasis is put on embedded manifold calculus (which is coordinate-free and relies on the embedding of a manifold into a larger ambient space). In addition, we also consider the control of non-linear systems whose states belong to curved manifolds. As a case study, synchronization of non-linear systems by feedback control on smooth manifolds (including Lie groups) is surveyed. Special emphasis is also put on numerical methods to simulate non-linear control systems on curved manifolds. The present tutorial is meant to cover a portion of the mentioned topics, such as first-order systems, but it does not cover topics such as covariant derivation and second-order dynamical systems, which will be covered in a subsequent tutorial paper.

scholarly journals Approximate Analyzing of Labeled Transition Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Qiong Yu ◽  
Shihan Yang ◽  
Jinzhao Wu
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Matrix Decomposition ◽  
Transition System ◽  
Formal Semantic ◽  
Semantic Model ◽  
Transition Systems ◽  
State Space Explosion ◽  
Normal Circumstance ◽  
Time Linear

As the most important formal semantic model, labeled transition systems are widely used, which can describe the general concurrent systems or control systems without disturbance. However, under normal circumstance, transition systems are complex and difficult to use due to large amount of calculation and the state space explosion problems. In order to overcome these problems, approximate equivalent labeled transition systems are proposed by means of incomplete low-up matrix decomposition factorization. This technique can reduce the complexity of computation and calculate under the allowing errors. As for continuous-time linear systems, we develop a modeling method of approximated transition system based on the approximate solution of matrix, which provides a facility for approximately formal semantic modeling for linear systems and to effectively analyze errors. An example of application in the context of linear systems without disturbances is studied.

On exact controllability of linear perturbed boundary systems: a semigroup approach

2020 ◽  
Vol 37 (4) ◽  
pp. 1548-1573
Author(s):  
Marieme Lasri ◽  
Hamid Bounit ◽  
Said Hadd
Keyword(s):  
Control System ◽  
Control Systems ◽  
Linear Systems ◽  
Banach Spaces ◽  
Exact Controllability ◽  
Dimensional Control ◽  
Neutral Equations ◽  
Infinite Dimensional ◽  
Semigroup Approach ◽  
Perturbed Linear Systems

Abstract The purpose of this paper is to investigate the robustness of exact controllability of perturbed linear systems in Banach spaces. Under some conditions, we prove that the exact controllability is preserved if we perturb the generator of an infinite-dimensional control system by appropriate Miyadera–Voigt perturbations. Furthermore, we study the robustness of exact controllability for perturbed boundary control systems. As application, we study the robustness of exact controllability of neutral equations. We mention that our approach is mainly based on the concept of feedback theory of infinite-dimensional linear systems.

scholarly journals Stability Analysis of Networked Control Systems Using a Switched Linear Systems Approach

2011 ◽  
Vol 56 (9) ◽  
pp. 2101-2115 ◽  
Author(s):  
M. C. F. Donkers ◽  
W. P. M. H. Heemels ◽  
Nathan van de Wouw ◽  
Laurentiu Hetel
Keyword(s):  
Stability Analysis ◽  
Control Systems ◽  
Linear Systems ◽  
Systems Approach ◽  
Networked Control Systems ◽  
Networked Control ◽  
Switched Linear Systems

scholarly journals Control systems with time lags

1976 ◽  
Vol 19 (4) ◽  
pp. 478-492 ◽  
Author(s):  
John M. Blatt
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Necessary Conditions ◽  
Time Lags ◽  
Optimal Controls ◽  
State Variables ◽  
Delayed Effects ◽  
Non Linear ◽  
Non Linear Systems

AbstractNecessary conditions for optimal controls are given for non-linear systems with time delayed effects in both control and state variables.

Lanekeeping at the Limits of Handling: Stability via Lyapunov Functions and a Comparison With Stability Control

2008 ◽  
Author(s):  
Kirstin L. R. Talvala ◽  
J. Christian Gerdes
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Lyapunov Functions ◽  
Stability Control ◽  
Tire Model ◽  
Quadratic Lyapunov Functions ◽  
Two Systems ◽  
Assistance Systems ◽  
Safety Systems

Lanekeeping assistance systems and stability control systems both seek to control the yaw behavior of the vehicle. However, lanekeeping systems are typically thought of as linear systems, while stability control systems are explicitly designed to work at the limits of handling. In order to bring these two systems together, there is a need to investigate lanekeeping up to and beyond the limits of handling. This paper presents a nonlinear tire model suitable for analyzing the behavior of a lanekeeping system at all points along the tire curve and a method for finding common quadratic Lyapunov functions to prove stability. The results show that the lanekeeping system is stable well into the nonlinear tire region. This stability holds even under changes in the lanekeeping gain and the understeering/oversteering characteristics of the vehicle. The results suggest that future safety systems could benefit from incorporating integrated lanekeeping and stability control functionality.

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