In this note, we deal with the exponential stability and stabilization problems for quadratic discrete-time systems with time delay. By using the quadratic Lyapunov function and a so called 'Finsler's lemma', delay-independent sufficient conditions for local stability and stabilization for quadratic discrete-time systems with time delay are derived in terms of linear matrix inequalities (LMIs). Based on these sufficient conditions, iterative linear matrix inequality algorithms are proposed for maximizing the stability regions of the systems. Finally, two examples are given to illustrate the effectiveness of the methods presented in this paper.

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We study the one-dimensional p-Laplacian m-point boundary value problemsome new results are obtained for the existence of at least one, two, and three positive solution/solutions of the above problem by using Krasnosel skll s fixed point theorem, new fixed point theorem due to Avery and Henderson, as well as Leggett-Williams fixed point theorem. This is probably the first time the existence of positive solutions of one-dimensional p-Laplacian mpoint boundary value problem on time scales has been studied.

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