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This paper concerns stability analysis and controller design for repetitive control. First, a two-dimensional (2D) continuous-discrete hybrid model of a repetitive control system is established. Next, new criteria for the asymptotic stability of the system are presented based on the model. Then, these criteria are extended to calculate lower bounds on(More)
The paper deals with the forced oscillation of the fractional differential equation (D q a x)(t) + f 1 (t, x(t)) = v(t) + f 2 (t, x(t)) for t > a ≥ 0 with the initial conditions (D q–k a x)(a) = b k (k = 1, 2,. .. , m – 1) and lim t→a + (I m–q a x)(t) = b m , where D q a x is the Riemann-Liouville fractional derivative of order q of x, m – 1 < q ≤ m, m ≥ 1(More)
The paper considers the oscillation of a second-order nonlinear dynamic equation with positive and negative coefficients of the form r(t)x (t) + p(t)f (x(ξ (t))) – q(t)h(x(δ(t))) = 0 on an arbitrary time scale T. We obtain some oscillation criteria for the equation by developing a generalized Riccati substitution technique. Our results extend and improve(More)
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