On necessary and sufficient conditions for time optimal control of second-order non-linear systems

1963 ◽  
Vol 1 (2) ◽  
pp. 300-305 ◽  
Author(s):  
E.B. Lee ◽  
L. Markus
Keyword(s):  
Optimal Control ◽  
Linear Systems ◽  
Sufficient Conditions ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Time Optimal Control ◽  
Non Linear ◽  
Time Optimal ◽  
Non Linear Systems ◽  
Necessary And Sufficient

Positive fractional continuous-time linear systems with singular pencils

2012 ◽  
Vol 60 (1) ◽  
pp. 9-12 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
State Variables ◽  
Algebraic Constraints ◽  
Necessary And Sufficient ◽  
Time Linear

Positive fractional continuous-time linear systems with singular pencils A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for the positivity of the fractional descriptor systems are established.

ON PROJECTIVELY RELATED WARPED PRODUCT FINSLER MANIFOLDS

2011 ◽  
Vol 08 (05) ◽  
pp. 953-967 ◽  
Author(s):  
M. M. REZAII ◽  
Y. ALIPOUR-FAKHRI
Keyword(s):  
Warped Product ◽  
Sufficient Conditions ◽  
Linear Connection ◽  
Necessary And Sufficient Conditions ◽  
Finsler Manifolds ◽  
Non Linear ◽  
Necessary And Sufficient

Let 𝔽1 = (M1,F1) and 𝔽2 = (M2,F2) be two Finsler manifolds and let M = M1 × M2 and S is a spray in M. Also 𝔽 = (M1 × f M2, F) is a warped product Finsler manifolds, such that the function f : M1 → ℝ+ is not constant. In this paper, we define a non-linear connection on warped product 𝔽, and finally, we have presented some necessary and sufficient conditions under which the spray manifold (M1 × M2, S) is projectively equivalent to the warped product Finsler manifolds (M1 × f M2, F).

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