In this paper, the stability and boundedness analysis of a certain system of two nonlinear delay differential equations with variable delay ρ(t) is carried out. By using the Lyapunov's second method and Lyapunov-Krasovskii's functional derived from the differential equations describing the system which yielded a better stability and boundedness estimate to establish sufficient conditions for the uniform asymptotic stability of the trivial solution and uniform ultimate boundedness of solution. These new results improve and generalize some results that can be found in the literature.

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This paper presents a stability and boundedness analysis of a system of RLC circuit modeled using a time varying state-space method. Stability problem analysis is very important in RLC circuits. There is some potential for a response characterizing the system of RLC circuit to approach infinity when subjected to certain types of inputs. Unstable circuit causes damage to electrical systems. Analysis of problems of such system stability is carried out using the Lyapunov's theory. In this paper, we provide in simple form, conditions which ensure the stability and boundedness of the state variables x i (t) (i = 1, 2) characterizing the system of RLC circuit using Lyapunov's second or direct method.