The article considers the methods of calculating the transition matrix of a dynamic system, which is based on the transient matrix representation by the matrix exponent and on the use of the system signal graph. The advantages of the transition matrix calculating using a signal graph are shown. The application of these methods to find the transition matrix demonstrated on the simple electromechanical system example.
This paper studies a finite-dimensional discrete linear system whose initial state $x_0$ is unknown. We assume that the system is augmented by two output equations, the first one $z_i$ being representing measurements made on the unknown state of the system and the other $y_i$ being representing the corresponding output. The purpose of our work is to introduce two control laws, both in closed-loop of measurements $z_i$ and whose goal is to reduce asymptotically the effects of the unknown part of the initial state $x_0$. The approach that we present consists of both th
This paper focuses on linear controlled discrete-time systems which subject to the control input disturbances. A disturbance is said to be admissible if the associated output function verifies the output constraints. In this paper, we address the following problem: determine the set of all admissible disturbances from all disturbances susceptible to the deformation of control input. An algorithm for computing the maximum admissible disturbances set is described and the sufficient conditions for finite termination of this algorithm are given.