E.N. Mahmudov
Controllability and observability of second order linear time invariant systems
In the present paper, controllability and observability of second order linear time invariant systems in matrix form are considered. Without reducing to first order systems, we show how the classical conditions for first order linear systems can be generalized to this case. In term of Kalman criteria, these concepts are investigated for second order discrete and continuous time linear systems. By repeated differentiation of state and output vector-functions, we derive two different systems of linear algebraic equations. Then the initial values x_0,x_1 and input functions can be determined uniquely from these systems if and only if the observability and controllability matrices have full rank, respectively. The transfer function of the second order continuous-time linear state-space system is also constructed. Numerical examples are presented to illustrate the theoretical results.
Keywords: Observability, Controllability, Second order, Kalman criterion, Difference operator
Controllability and observability of second order linear time invariant systems
In the present paper, controllability and observability of second order linear time invariant systems in matrix form are considered. Without reducing to first order systems, we show how the classical conditions for first order linear systems can be generalized to this case. In term of Kalman criteria, these concepts are investigated for second order discrete and continuous time linear systems. By repeated differentiation of state and output vector-functions, we derive two different systems of linear algebraic equations. Then the initial values x_0,x_1 and input functions can be determined uniquely from these systems if and only if the observability and controllability matrices have full rank, respectively. The transfer function of the second order continuous-time linear state-space system is also constructed. Numerical examples are presented to illustrate the theoretical results.
Keywords: Observability, Controllability, Second order, Kalman criterion, Difference operator