In this paper, we study the instability of the zero solution to a nonlinear differential equation with variable delay. By using the Lyapunov functional approach, some sufficient conditions for instability of the zero solution are obtained. Keywords—Instability, Lyapunov-Krasovskii functional, delay differential equation, fifth order.

In this paper, by using majorization inequalities, upper bounds on summations of eigenvalues (including the trace) of the solution for the Lyapunov matrix differential equation are obtained. In the limiting cases, the results reduce to bounds of the algebraic Lyapunov matrix equation. The effectiveness of the results are illustrated by numerical examples.

In this paper, by using majorization inequalities, upper bounds on summations of eigenvalues (including the trace) of the solution for the Lyapunov matrix differential equation are obtained. In the limiting cases, the results reduce to bounds of the algebraic Lyapunov matrix equation. The effectiveness of the results are illustrated by numerical examples.

In this paper, an iterative technique is proposed to solve linear integrated active/passive design problems. The optimality of active and passive parts leads to the nonlinear algebraic Riccati equation due to the active parameters and some associated additional Lyapunov equations due to the passive parameters. Rather than the solution of the nonlinear algebraic Riccati equation, it is proposed ...

In the present paper an H∞ control design is presented for DC-DC Ćuk converter using its average model. Lyapunov equation is used to derivate the controller and to estimate the L2 gain too. Theoretical result is supported by numerical simulations. Key-Words: H∞ control, PWM, Lyapunov equation, Ćuk converter.

In recent years, several bounds have been reported for different measures of the “extent” or “size” of the solution of the algebraic matrix equation arising in control theory, such as the Riccati equation and the Lyapunov equation. This paper collects the bounds that have been presented up to now and summarizes them in an unified form. This will prove particularly convenient for those wishing t...

For discrete-time descriptor syslems, various generalized Lyapunov equations were studied in the literature. Howevn these well known generalized Lyapunov equations can be used only under some restrictive assumptions on the plant (as system regularity, or positiveness of a Q matrix, for example). To overcome these limitations, we propose in this paper a new generalized Lyapunov equation for disc...

We develop an approach to the construction of Lyapunov functions for the forward equation of a nite state nonlinear Markov process. Nonlinear Markov processes can be obtained as a law of large number limit for a system of weakly interacting processes. The approach exploits this connection and the fact that relative entropy de nes a Lyapunov function for the solution of the forward equation for ...