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In this article, we establish some sufficient conditions for the complete controllability of semilinear matrix Lyapunov systems involving Lipschitzian and non-Lipschitzian nonlinearities. In case of non-Lipschitzian nonlinearities, we assume that nonlinearities are of monotone type. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the controllability of a system described by an integral inclusion of Urysohn type with delay. In our approach we reduce the controllability problem of the nonlinear system into solvability problem of another integral inclusion. The solvability of this integral inclusion is subsequently established by imposing suitable standard boundedness, convexity and semicontinuity conditions on the set-valued mapping defining the integral inclusion, and by employing Bohnenblust-Karlin extension of Kakutani's fixed point theorem for set-valued mappings. [ABSTRACT FROM AUTHOR]

Many of the real life problems are modelled as Matrix Second Order Systems, (refer Wu and Duan [19], Hughes and Skelton [10]). Necessary and sufficient condition for controllability of Matrix Second Order Linear (MSOL) Systems has been established by Hughes and Skelton [10]. However, no scheme for computation of control was proposed. In this paper we first obtain another necessary and sufficient condition for the controllability of MSOL and provide a computational algorithm for the actual computation of steering control. We also consider a class of Matrix Second Order Nonlinear systems (MSON) and provide sufficient conditions for its controllability. In our analysis we make use of Sine and Cosine matrices and employ Páde approximation for the computation of matrix Sine and Cosine. We also invoke tools of nonlinear analysis like fixed point theorem to obtain controllability result for the nonlinear system. We provide numerical example to substantiate our results. [ABSTRACT FROM AUTHOR]

In this article, we study the exact controllability of an abstract model described by the controlled generalized Hammerstein type integral equation x(t) = Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. h(t, s)u(s)ds + Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. k(t, s, x)f(s, x(s))ds, 0 ≤ t ≤ T < ∞, where, the state x(t) lies in a Hilbert space H and control u(t) lies another Hilbert space V for each time t ∈ I = [0, T], T > 0. We establish the controllability result under suitable assumptions on h, k and f using the monotone operator theory. [ABSTRACT FROM AUTHOR]