Comptes rendus de l’Acade'mie bulgare des Sciences, Vol 66, No8, pp.1167-1174
## Infinite Horizon LQR Problem of Linear Discrete Time Positive Systems

### Snezhana Kostova, Ivan Ivanov, Lars Imsland, Nonka Georgieva

## ABSTRACT

The optimal control problems for positive systems is an important and extensively studied topic in recent years. In this paper, the infinite horizon LQR problem of positive linear discrete time systems (PLDS) is studied. For solving the problem we consider the approach based on the admissibility of the solution of the standard infinite discrete LQR problem. We use the well-known from the literature solution of the problem based on the solution of the discrete matrix algebraic Riccati equation. We find additional sufficient conditions on the system and weight matrices which guarantee stability, optimality and positiveness of the system. The numerical example is given for illustration of the result.

**Key words: **positive systems, optimization, Riccati equation

Topic: ENGINEERING SCIENCES