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New stability tests for positive descriptor linear systems

Kaczorek Tadeusz

Bulletin of the Polish Academy of Sciences. Technical Sciences

2022

Vol. 70, nr 3

art. no. e140688

The asymptotic stability of positive descriptor continuous-time and discrete-time linear systems is considered. New sufficient conditions for stability of positive descriptor linear systems are established. The efficiency of the new stability conditions are demonstrated on numerical examples of continuous-time and discrete-time linear systems.

On connected functions in ordered spaces

Jędrzejewski J.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2010

Vol. 15

51--58

We consider some properties of functions defined in a topological space X with values in a topological space Y. The definitions 1, 2 and 3 define the same class of functions when X and Y are equal to R with natural topology. In this article we discuss some properties of those classes and give some sufficient conditions for the space X in which real functions defined in X form the same class.

Semiinfinite multiobjective fractional programming. Part I: Sufficient efficiency conditions

Zalmai G. J., Zhang Q.

Journal of Applied Analysis

2010

Vol. 16, nr 2

199-224

In this paper, we formulate and discuss a fairly large number of sets of global parametric sufficient efficiency criteria under various generalized (η, ρ)-invexity assumptions, and prove a semiinfinite version of a well-known second-order sufficiency result for a semiinfinite multiobjective fractional programming problem.

Sufficient conditions and duality for multiobjective variational problems with generalized B-invexity

Aghezzaf B., Khazafi K.

Control and Cybernetics

2004

Vol. 33, no 1

113-126

In this paper, we consider the multiobjective variational problem. We propose a class of generalized B-type I vector-valued functions and use this concept to establish sufficient optimality conditions and mixed type duality results

Theconjugate points sufficient conditions for an optimal control

Szymanowska A.

Control and Cybernetics

1998

Vol. 27, no 3

353-362

The paper concerns an application of the idea of field theory and the concept of "concourse of flights" to the sufficient optimality conditions for the optimal control problems stated in terms of focal and conjugate points. The concept of concourse of flights was begun by Young (1969), and later extended by Nowakowski (1988). In the paper the definition of a focal and conjugate point of a field of extremals is given. Using these concepts, we prove that the existence of a field of extremals without conjugate points implies the existence of concourse of flights and consequently we obtain the second order sufficient conditions for the generalized problem of Bolza. Another approach to the concept of focal and conjugate points is given by Zeidan (1983, 1984).