scholarly journals An optimization problem for infinite order distributed parabolic systems with multiple time-varying lags

2013 ◽  
Vol 7 (3) ◽  
pp. 146-161
Author(s):  
G.M. Bahaa
Keyword(s):  
Optimization Problem ◽  
Infinite Order ◽  
Parabolic Systems ◽  
Multiple Time ◽  
Time Varying

scholarly journals Optimality Conditions for Infinite Order Distributed Parabolic Systems with Multiple Time Delays Given in Integral Form

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Bahaa G. M.
Keyword(s):  
Optimality Conditions ◽  
Time Delays ◽  
Infinite Order ◽  
Neumann Boundary ◽  
Integral Form ◽  
Parabolic Systems ◽  
Multiple Time ◽  
State Equations ◽  
Multiple Time Delays ◽  
Performance Functional

The optimal boundary control problem for (n×n) infinite order distributed parabolic systems with multiple time delays given in the integral form both in the state equations and in the Neumann boundary conditions is considered. Constraints on controls are imposed. Necessary and suffacient optimality conditions for the Neumann problem with the quadratic performance functional are derived.

Robust stability and memory state feedback control for a class of switched nonlinear systems with multiple time-varying delays

2021 ◽  
pp. 107754632098598
Author(s):  
Marwen Kermani ◽  
Anis Sakly
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Multiple Time ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Common Lyapunov Function ◽  
Suggested Approach ◽  
Aggregation Techniques

This study is concerned with the stability analysis and the feedback stabilization problems for a class of uncertain switched nonlinear systems with multiple time-varying delays. Unusually, more general time delays, which depend on the subsystem number, are considered. In this regard, by constructing a novel common Lyapunov function, using the aggregation techniques and the Borne and Gentina criterion, new algebraic stability and feedback stabilization conditions under arbitrary switching are derived. The proposed results are explicit and obtained without searching a common Lyapunov function through the linear matrix inequalities approach, considered a difficult matter in this case. At last, two numerical simulation examples are shown to prove the practical utility of the suggested approach.

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