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Exponential estimates of a class of time-delay nonlinear systems with convex representations

Ramírez M., Villafuerte R., González T., Bernal M.

International Journal of Applied Mathematics and Computer Science

2015

Vol. 25, no. 4

815--826

This work introduces a novel approach to stability and stabilization of nonlinear systems with delayed multivariable inputs; it provides exponential estimates as well as a guaranteed cost of the system solutions. The result is based on an exact convex representation of the nonlinear system which allows a Lyapunov–Krasovskii functional to be applied in order to obtain sufficient conditions in the form of linear matrix inequalities. These are efficiently solved via convex optimization techniques. A real-time implementation of the developed approach on the twin rotor MIMO system is included.

Exponent in one of the variables

Mityushev V.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2007

Vol. 12

77-79

A periodicity functional equation of one complex variable which characterizes the exponential function is discussed. This functional equation can be generalized to equation for functions depending on two complex variables. It is conjectured that the second functional equation also characterizes the exponent. Applications to representations of complex continuous elementary functions are discussed.