2019/06/16 by Elimhan N. Mahmudov, Mahmudov, Elimhan N.
Computer Science · Engineering · #11D04 #39A70 #93B05 #93B07 #Adaptive Control of Nonlinear Systems #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.1906.06741
openalex publication_date 2019/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper we consider controllability and observability of second order linear time invariant systems in matrix form. Without reducing into first order systems we show how the classical conditions for first order linear systems can be generalized to this case. In term of Kalman type criterions these concepts are investigated for second order discrete and continuous time linear systems. It should be pointed out that by repeated differentiation of state and output vector-functions we derive two different systems of linear algebraic equations. Then the initial values x0, x1 and input functions can be determined uniquely from these systems if and only if the observability and controllability matrices have full rank, respectively. Also the transfer function of the second order continuous-time linear state-space system is constructed. A numerical example is given to illustrate the feasibility and effectiveness of the theoretic results obtained.