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2 International Journal of Applied Mathematics and Computer Science

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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.

Non-quadratic performance design for Takagi-Sugeno fuzzy systems

Bernal M., Husek P.

International Journal of Applied Mathematics and Computer Science

2005

Vol. 15, no 3

383-391

This paper improves controller synthesis of discrete Takagi-Sugeno fuzzy systems based on non-quadratic Lyapunov functions, making it possible to accomplish various kinds of control performance specifications such as decay rate conditions, requirements on control input and output and disturbance rejection. These extensions can be implemented via linear matrix inequalities, which are numerically solvable with commercially available software. The controller design is illustrated with an example.