The Stabilization of Switched Systems with Input Saturation

2014 ◽  
Vol 945-949 ◽  
pp. 2676-2679
Author(s):  
Li Jing ◽  
Li Liu
Keyword(s):  
Switched Systems ◽  
Convex Combination ◽  
Input Saturation ◽  
Switched System ◽  
New Method ◽  
Combination Method ◽  
Sufficient Condition ◽  
The Stability ◽  
Special Case ◽  
Convex Combination Method

The paper analyzed the stability of switched systems with input saturation. First it considered a special case: the switched system with only one subsystem. Using a new method to dispose saturation in the system, the paper gets the sufficient condition of stability of the system. Based on the result, the controller of the system is designed. Then common switched systems were studied. By convex combination method we obtain the sufficient conditon of stability of switched systems and propose a method to estimate the attration domain of the systems.

The Stabilization of Switched Time-Delay Linear Systems with Input Saturation

2014 ◽  
Vol 602-605 ◽  
pp. 2582-2585
Author(s):  
Li Jing ◽  
Li Liu
Keyword(s):  
Time Delay ◽  
Lyapunov Function ◽  
Linear Systems ◽  
Input Saturation ◽  
Switched System ◽  
New Method ◽  
System Stability ◽  
Sufficient Condition ◽  
Switched Linear Systems ◽  
System Controller

We focused on the stabilization of switched linear systems with time-delay and input saturation. First, the saturation part of each subsystem was dealt with by a new method and the system was transformed into a general switched system. Secondly, we proposed a sufficient condition for system stability based on Multi - Lyapunov Function. The sufficient condition is expressed into LMI and can be solved with MatLab. Further, we designed the system controller.

Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

1995 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Axial Direction ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

scholarly journals Stability Analysis for Autonomous Dynamical Switched Systems through Nonconventional Lyapunov Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
V. Nosov ◽  
J. A. Meda-Campaña ◽  
J. C. Gomez-Mancilla ◽  
J. O. Escobedo-Alva ◽  
R. G. Hernández-García
Keyword(s):  
Stability Analysis ◽  
Finite Number ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Switched System ◽  
Linear Functions ◽  
Asymptotically Stable ◽  
Multiple Lyapunov Functions ◽  
Stability Theorems ◽  
The Stability

The stability of autonomous dynamical switched systems is analyzed by means of multiple Lyapunov functions. The stability theorems given in this paper have finite number of conditions to check. It is shown that linear functions can be used as Lyapunov functions. An example of an exponentially asymptotically stable switched system formed by four unstable systems is also given.

scholarly journals Stability Criteria of Interval Time-Varying Delay Systems and Their Application

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Zhanhui Lu ◽  
Chengyong Wang ◽  
Weijuan Wang
Keyword(s):  
Convex Combination ◽  
Combination Method ◽  
Delay Systems ◽  
Time Varying ◽  
Stability Criteria ◽  
Interval Time ◽  
Time Varying Delay ◽  
The Stability ◽  
Delay Dependent ◽  
Uncertain Linear Systems

The stability for a class of uncertain linear systems with interval time-varying delays is studied. Based on the delay-dividing approach, the delay interval is partitioned into two subintervals. By constructing an appropriate Lyapunov-Krasovskii functional and using the convex combination method and the improved integral inequality, the delay-dependent stability criteria with less conservation are derived. Finally, some numerical examples are given to show the effectiveness and superiority of the proposed method.

Robot Trajectory Control System Design for Multiple Simultaneous Specifications: Theory and Experimentation

1998 ◽  
Vol 120 (4) ◽  
pp. 520-523 ◽  
Author(s):  
Hugh H. T. Liu ◽  
James K. Mills
Keyword(s):  
Control System ◽  
Steady State ◽  
Design Method ◽  
Convex Combination ◽  
External Disturbance ◽  
Control Design ◽  
Combination Method ◽  
Control System Design ◽  
Robot Trajectory ◽  
Convex Combination Method

A new control design method is developed to satisfy multiple specifications simultaneously. The proposed convex combination method is applied to a six (6)-degree-of-freedom commercial robot. In a trajectory tracking task under external disturbance, four requirements, stability, path accuracy, velocity accuracy, and steady-state error of position, can be met at the same time. The experimental results verify this conclusion.

Existence of Periodic Solution for Beams With Harmonically Variable Length

1997 ◽  
Vol 119 (3) ◽  
pp. 485-488 ◽  
Author(s):  
E. Esmailzadeh ◽  
G. Nakhaie-Jazar ◽  
B. Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Longitudinal Axis ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

The transverse oscillatory motion of a simple beam with one end fixed while driven harmonically at the other end along its longitudinal axis is investigated. For a special case of zero value for the rigidity of beam, the problem reduces to that of a vibrating string with its corresponding equation of motion. The sufficient condition for the periodic solution of the beam was determined using the Green’s function and Schauder’s fixed point theorem. The criterion for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

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