scholarly journals Application of hybrid and polytopic modeling to the stability analysis of linear systems with saturating inputs

2004 ◽  
Vol 15 (4) ◽  
pp. 401-412 ◽  
Author(s):  
J.M. Gomes da Silva Jr ◽  
S. Tarbouriech ◽  
R. Reginatto
Keyword(s):  
Stability Analysis ◽  
Linear Systems ◽  
Critical Analysis ◽  
Actuator Saturation ◽  
Hybrid Modeling ◽  
Stability Regions ◽  
The Stability

This paper is concerned with the problem of stability regions determination for linear systems with saturating inputs. The paper focuses on a critical analysis of two known approaches to model the effect of actuator saturation: hybrid modeling and polytopic modeling. In each case, algorithms to determine ellipsoidal domains of stability for such class of systems are provided in terms of LMIs. The ability of such algorithms in providing large stability domains is analyzed by highlighting the main reasons they incorporate conservativeness, including the influence of the saturation modeling. Two examples are worked out illustrating how significantly the stability domains obtained by such algorithms can differ.

scholarly journals Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems

2012 ◽  
Vol 22 (2) ◽  
pp. 401-408 ◽  
Author(s):  
Mikołaj Busłowicz ◽  
Andrzej Ruszewski
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Linear Systems ◽  
Type Model ◽  
Stability Tests ◽  
Numerical Examples ◽  
Computer Methods ◽  
Discrete Linear Systems ◽  
Complex Functions ◽  
The Stability

Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systemsAsymptotic stability of models of 2D continuous-discrete linear systems is considered. Computer methods for investigation of the asymptotic stability of the Roesser type model are given. The methods require computation of eigenvalue-loci of complex matrices or evaluation of complex functions. The effectiveness of the stability tests is demonstrated on numerical examples.

scholarly journals An iterative frequency-sweeping approach for stability analysis of linear systems with multiple delays

2017 ◽  
Vol 36 (2) ◽  
pp. 379-398
Author(s):  
Xu-Guang Li ◽  
Silviu-Iulian Niculescu ◽  
Arben Çela
Keyword(s):  
Stability Analysis ◽  
Asymptotic Behaviour ◽  
Linear Systems ◽  
Invariance Property ◽  
Multiple Delays ◽  
Numerical Examples ◽  
The Stability ◽  
Imaginary Roots ◽  
Frequency Sweeping

AbstractIn this article, we study the stability of linear systems with multiple (incommensurate) delays, by extending a recently proposed frequency-sweeping approach. First, we consider the case where only one delay parameter is free while the others are fixed. The complete stability w.r.t. the free delay parameter can be systematically investigated by proving an appropriate invariance property. Next, we propose an iterative frequency-sweeping approach to study the stability under any given multiple delays. Moreover, we may effectively analyse the asymptotic behaviour of the critical imaginary roots (if any) w.r.t. each delay parameter, which provides a possibility for stabilizing the system through adjusting the delay parameters. The approach is simple (graphical test) and can be applied systematically to the stability analysis of linear systems including multiple delays. A deeper discussion on its implementation is also proposed. Finally, various numerical examples complete the presentation.

Stability and controllability of switched systems

2013 ◽  
Vol 61 (3) ◽  
pp. 547-555 ◽  
Author(s):  
J. Klamka ◽  
A. Czornik ◽  
M. Niezabitowski
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Linear Systems ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Switched Linear Systems ◽  
Arbitrary Switching ◽  
Mathematical Problems ◽  
The Stability ◽  
Necessary And Sufficient

Abstract The study of properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. This paper aims to briefly survey recent results on stability and controllability of switched linear systems. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After that, we review the controllability results.

scholarly journals Common Weak Linear Copositive Lyapunov Functions for Positive Switched Linear Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Yuangong Sun ◽  
Zhaorong Wu ◽  
Fanwei Meng
Keyword(s):  
Stability Analysis ◽  
Complex Systems ◽  
Linear Systems ◽  
Algebraic Structure ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Switched Linear Systems ◽  
Numerical Examples ◽  
The Stability ◽  
Necessary And Sufficient

Lyapunov functions play a key role in the stability analysis of complex systems. In this paper, we study the existence of a class of common weak linear copositive Lyapunov functions (CWCLFs) for positive switched linear systems (PSLSs) which generalize the conventional common linear copositive Lyapunov functions (CLCLFs) and can be used as handy tool to deal with the stability of PSLSs not covered by CLCLFs. We not only establish necessary and sufficient conditions for the existence of CWCLFs but also clearly describe the algebraic structure of all CWCLFs. Numerical examples are also given to demonstrate the effectiveness of the obtained results.

An Anti-Windup Design for Linear System With Asymptotic Tracking Subjected to Actuator Saturation

1998 ◽  
Vol 122 (2) ◽  
pp. 369-374 ◽  
Author(s):  
Weiguang Niu ◽  
Masayoshi Tomizuka
Keyword(s):  
Control System ◽  
Linear System ◽  
Linear Systems ◽  
Motion Control ◽  
Output Feedback ◽  
System Performance ◽  
Actuator Saturation ◽  
Lyapunov Stability Theory ◽  
Asymptotic Tracking ◽  
The Stability

This paper deals with asymptotic tracking for linear systems with actuator saturation in the presence of disturbances. Both reference inputs and disturbances are assumed to belong to a class which may be regarded as the zero-input responses of linear systems. The controller includes an anti-windup term which reduces the degradation in the system performance due to saturation. The stability of the overall system is established based on the Lyapunov stability theory. Both state and output feedback solutions are given. The proposed scheme is evaluated for a two axis motion control system by simulation. [S0022-0434(00)01002-9]

Neural control of robot manipulators considering motor voltage saturation: performance evaluation and experimental validation

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Alireza Izadbakhsh ◽  
Saeed Khorashadizadeh
Keyword(s):  
Performance Evaluation ◽  
Stability Analysis ◽  
Neural Control ◽  
Actuator Saturation ◽  
Tracking Error ◽  
Design Procedure ◽  
Content Type ◽  
Electrical Motors ◽  
The Stability ◽  
Voltage Saturation

Purpose This paper aims to design a neural controller based on radial basis function networks (RBFN) for electrically driven robots subjected to constrained inputs. Design/methodology/approach It is assumed that the electrical motors have limitations on the applied voltages from the controller. Due to the universal approximation property of RBFN, uncertainties including un-modeled dynamics and external disturbances are represented with this powerful neural network. Then, the lumped uncertainty including the nonlinearities imposed by actuator saturation is introduced and a mathematical model suitable for model-free control is presented. Based on the closed-loop equation, a Lyapunove function is defined and the stability analysis is performed. It is assumed that the electrical motors have limitations on the applied voltages from the controller. Findings A comparison with a similar controller shows the superiority of the proposed controller in reducing the tracking error. Experimental results on a SCARA manipulator actuated by permanent magnet DC motors have been presented to guarantee its successful practical implementation. Originality/value The novelty of this paper in comparison with previous related works is improving the stability analysis by involving the actuator saturation in the design procedure. It is assumed that the electrical motors have limitations on the applied voltages from the controller. Thus, a comprehensive approach is adopted to include the saturated and unsaturated areas, while in previous related works these areas are considered separately. Moreover, a performance evaluation has been carried out to verify satisfactory performance of transient response of the controller.

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