scholarly journals Sufficient conditions for asymptotic stability and feedback control of set dynamical systems

2017 ◽  
Author(s):  
Nathalie Risso ◽  
Ricardo G. Sanfelice
Keyword(s):  
Dynamical Systems ◽  
Feedback Control ◽  
Asymptotic Stability ◽  
Sufficient Conditions

On the Almost Sure Stability of Linear Stochastic Distributed-Parameter Dynamical Systems

1966 ◽  
Vol 33 (1) ◽  
pp. 182-186 ◽  
Author(s):  
P. K. C. Wang
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Integral Equations ◽  
Sufficient Conditions ◽  
Distributed Parameter ◽  
Almost Sure Stability ◽  
Partial Differential ◽  
Stochastic Parameters

In this paper, sufficient conditions for almost sure stability and asymptotic stability of certain classes of linear stochastic distributed-parameter dynamical systems are derived. These systems are described by a set of linear partial differential or differential-integral equations with stochastic parameters. Various examples are given to illustrate the application of the main results.

scholarly journals Hybrid nonnegative and computational dynamical systems

2002 ◽  
Vol 8 (6) ◽  
pp. 493-515 ◽  
Author(s):  
Wassim M. Haddad ◽  
Vijaysekhar Chellaboina ◽  
Sergey G. Nersesov
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Conservation Laws ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Hybrid Structures ◽  
Stability Criteria ◽  
General Stability ◽  
Feedback Interconnections ◽  
Flow Laws

Nonnegative and Compartmental dynamical systems are governed by conservation laws and are comprised of homogeneous compartments which exchange variable nonnegative quantities of material via intercompartmental flow laws. These systems typically possess hierarchical (and possibly hybrid) structures and are remarkably effective in capturing the phenomenological features of many biological and physiological dynamical systems. In this paper we develop several results on stability and dissipativity of hybrid nonnegative and Compartmental dynamical systems. Specifically, usinglinearLyapunov functions we develop sufficient conditions for Lyapunov and asymptotic stability for hybrid nonnegative dynamical systems. In addition, usinglinearandnonlinearstorage functions withlinearhybrid supply rates we developnewnotions of dissipativity theory for hybrid nonnegative dynamical systems. Finally, these results are used to develop general stability criteria for feedback interconnections of hybrid nonnegative dynamical systems.

scholarly journals Rate Estimation of Identical Synchronization by Designing Controllers

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Mitul Islam ◽  
Bipul Islam ◽  
Nurul Islam
Keyword(s):  
Dynamical Systems ◽  
Feedback Control ◽  
Chaotic System ◽  
Tracking Control ◽  
Sufficient Conditions ◽  
Graphical Analysis ◽  
Control Technique ◽  
Chaotic Dynamical Systems ◽  
Necessary And Sufficient ◽  
Maximum Minimum

This paper investigates the synchronization rate for identical synchronization of chaotic dynamical systems, achieved by using controllers. The paper stresses on the hybrid feedback control technique and the tracking control technique and determines their corresponding maximum, minimum, and average synchronization rates. The results obtained are applied on the Shimizu-Morioka chaotic system, and some necessary and sufficient conditions for synchronization are obtained. Comparison of the two controllers is undertaken on the basis of their synchronization rates, in the context of the Shimizu-Morioka system. The results are analyzed both theoretically and numerically. Moreover, a method of graphical analysis is proposed to completely characterize the set of hybrid controllers for a given system.

Stability of nonlinear output‐feedback control system

Kybernetes ◽  
2004 ◽  
Vol 33 (2) ◽  
pp. 347-354 ◽  
Author(s):  
Guangxing Tan ◽  
Jian Pan
Keyword(s):  
Control System ◽  
Feedback Control ◽  
Asymptotic Stability ◽  
Nonlinear Control ◽  
Output Feedback ◽  
Sufficient Conditions ◽  
Liapunov Function ◽  
Output Feedback Control ◽  
Feedback Control System ◽  
The Stability

This paper studies the stability properties of a class of nonlinear output‐feedback control system. By using a control transform and constructing Liapunov function, the sufficient conditions of the asymptotic stability for the nonlinear control system are presented. The result in this paper includes some existing results.

Universal Feedback Controllers and Inverse Optimality for Nonlinear Stochastic Systems

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Wassim M. Haddad ◽  
Xu Jin
Keyword(s):  
Dynamical Systems ◽  
Feedback Control ◽  
Stochastic Control ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Optimal Feedback Control ◽  
Control Law ◽  
Stochastic Dynamical Systems ◽  
Control Lyapunov Function ◽  
Inverse Optimality

Abstract In this paper, we develop a constructive finite time stabilizing feedback control law for stochastic dynamical systems driven by Wiener processes based on the existence of a stochastic control Lyapunov function. In addition, we present necessary and sufficient conditions for continuity of such controllers. Moreover, using stochastic control Lyapunov functions, we construct a universal inverse optimal feedback control law for nonlinear stochastic dynamical systems that possess guaranteed gain and sector margins. An illustrative numerical example involving the control of thermoacoustic instabilities in combustion processes is presented to demonstrate the efficacy of the proposed framework.

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