Construction and analysis of mathematical models in state space for a cardiac pacemaker control system

A. V. Tsyganov^a, J. V. Tsyganova^abc, R. I. Rakhimova<sup>a

a</sup> Ul'yanovsk State Pedagogical University, Russia
^b Innopolis University, Russia
^c Ulyanovsk State University, Russia

Abstract: The paper considers the solution to the problem of constructing mathematical models of a pacemaker control system. Based on the existing structural scheme and the corresponding transfer function, mathematical models were constructed, presented in the state space in continuous and discrete time of the following forms: standard controllable form, standard observable form, canonical form. The properties of complete controllability and complete observability of the obtained mathematical models were studied depending on the model parameter K. A specially developed script in the symbolic computing language Maple was used to accelerate and automate the calculations. The results obtained will be used in the future to construct the corresponding stochastic models in order to solve the problem of parameter identification of the mathematical model of the pacemaker control system in the presence of random noises in the state and measurement equations.

Keywords: cardiac pacemaker control system, mathematical model in state space, controllability, observability

UDC: 681.5.075

Received: 24.09.2024
Revised: 11.12.2024