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In the present paper we consider controllability and observability of secondorder linear time invariant systems in matrix form. Without reducing into firstorder systems we show how the classical conditions for first order linearsystems can be generalized to this case. In term of Kalman type criterionsthese concepts are investigated for second order discrete and continuous timelinear systems. It should be pointed out that by repeated differentiation ofstate and output vector-functions we derive two different systems of linearalgebraic equations. Then the initial values x_0, x_1 and input functions canbe determined uniquely from these systems if and only if the observability andcontrollability matrices have full rank, respectively. Also the transferfunction of the second order continuous-time linear state-space system isconstructed. A numerical example is given to illustrate the feasibility andeffectiveness of the theoretic results obtained.

Observability and Controllability of Second Order Linear Time Invariant Systems and Kalman Type Conditions