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This article considers a class of finite-dimensional linear impulsive time-varying systems for which various sufficient and necessary algebraic criteria for complete controllability, including matrix rank conditions are established. The obtained controllability results are further synthe- sised for the time-invariant case, and under some special conditions on the system parameters, we obtain a Popov-Belevitch-Hautus (PBH)-type rank condition which employs eigenvalues of the system matrix for the investigation of their controllability. Numerical examples are pro- vided that demonstrate|for the linear impulsive systems, null controllability need not imply their complete controllability, unlike for the non-impulsive linear systems. [ABSTRACT FROM AUTHOR]

In this paper, we establish some sufficient conditions for the complete controllability of linear and semilinear impulsive systems. For the semilinear systems, we assume that nonlinearities are Lipschitzian type. We invoke the tools of nonlinear functional analysis and fixed point theorems to establish the results. The results are also compared with the existing results in the literature in order to show the effectiveness of the results obtained. Few illustrative examples are provided to substantiate the results. [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]