A new approach to LQ time-varying controllers with terminal equality constraints

2013 ◽  
Vol 43 (4) ◽  
pp. 549-556
Author(s):  
WanXie ZHONG ◽  
ShuJun TAN ◽  
ZhiGang WU
Keyword(s):  
Equality Constraints ◽  
Time Varying ◽  
New Approach ◽  
Terminal Equality Constraints

Control of Nonlinear Systems in Normal Form by Complementary Lyapunov Functions

2017 ◽  
Author(s):  
Andy Zelenak ◽  
Benito Fernández ◽  
Mitch Pryor
Keyword(s):  
Lyapunov Function ◽  
Normal Form ◽  
Lyapunov Functions ◽  
General Type ◽  
Order System ◽  
Time Varying ◽  
Control Lyapunov Function ◽  
New Approach ◽  
Complementary Function ◽  
Siso Systems

If a Lyapunov function is known, a dynamic system can be stabilized. However, the search for a Lyapunov function is often challenging. This paper takes a new approach to avoid such a search; it assumes a basic Control Lyapunov Function [CLF] then seeks to numerically diminish the value of the Lyapunov function. If a singularity arises during calculations with the default CLF, a complementary function is used. The complementary function eliminates a common cause of singularities with the default CLF. While many other algorithms from the literature use switched or time-varying CLF’s, the presented method is unique in that the CLF’s do not require prior calculation and the technique applies globally. The method is proven and demonstrated for SISO systems in normal form and then demonstrated on a higher-order system of a more general type.

FURTHER RESULTS ON MASTER-SLAVE SYNCHRONIZATION OF GENERAL LUR'E SYSTEMS WITH TIME-VARYING DELAY

2008 ◽  
Vol 18 (01) ◽  
pp. 187-202 ◽  
Author(s):  
FERNANDO O. SOUZA ◽  
REINALDO M. PALHARES ◽  
EDUARDO M. A. M. MENDES ◽  
LEONARDO A. B. TÔRRES
Keyword(s):  
Communication Systems ◽  
Functional Differential Equations ◽  
Linear Matrix ◽  
Time Varying ◽  
Lur’E Systems ◽  
New Approach ◽  
Time Varying Delay ◽  
Delay Feedback Control ◽  
Functional Differential ◽  
Varying Delay

In this paper, a new approach to analyze the asymptotic, exponential and robust stability of the master-slave synchronization for Lur'e systems using time-varying delay feedback control is proposed. The discussion is motivated by the problem of transmitting information in optical communication systems using chaotic lasers. The approach is based on the Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique with the use of a recent Leibniz–Newton model based transformation, without including any additional dynamics. Using the problem of synchronizing coupled Chua's circuits, three examples are given to illustrate the effectiveness of the proposed methodology.

Structural Decomposition Approach for the Stability of Uncertain Dynamic Systems

1988 ◽  
Vol 55 (4) ◽  
pp. 992-994 ◽  
Author(s):  
Y. H. Chen ◽  
Chieh Hsu
Keyword(s):  
Dynamic Systems ◽  
A Priori ◽  
Parameter Variation ◽  
Stability Study ◽  
Fast Time ◽  
Time Varying ◽  
Decomposition Approach ◽  
New Approach ◽  
Uncertain Dynamic Systems ◽  
The Stability

The stability property for a class of dynamic systems with uncertain parameter variation is studied. The uncertainty can be fast time-varying and unpredictable. A new approach for stability study is proposed. The only required information on the uncertain variation is its possible bound as well as structure. That is, no a priori knowledge on the realization of the variation is needed.

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