Abstract—This paper proposes a new H-infinity quadratic tracking control (QTC) algorithm in linear discretetime systems. This algorithm is a counterpart of the H-infinity QTC algorithm in linear continuous-time systems based on the integral equation approach. The discrete-time state equation in this paper has the control and exogenous inputs. Theorem 1 shows that the control and exogenous inputs in the H-infinity linear QTC problem are given by solving the two-point boundary value problem (TPBVP). Based on the TPBVP, Theorem 2 presents the H-infinity linear QTC algorithm for the control and exogenous inputs. The inputs use the information of two functions, which are calculated in the reverse direction of time from their terminal conditions. The control and exogenous inputs use the information of the state. The state observer uses the output of the system to estimate the state. A numerical simulation example shows the tracking control characteristics of the output estimate to the desired value and the characteristics of the estimates of the control and exogenous inputs. For the infinite value of the constant disturbance attenuation level γ, the proposed H-infinity linear QTC algorithm reduces to the linear QTC algorithm. The problem that can be solved for the minimum value of γ is the H-infinity linear QTC problem. For smaller value than the minimum value of γ, the H-infinity linear QTC algorithm diverges.

**Keywords:** H-infinity linear tracking control; Control input; Exogenous input; State observer; Discrete-time systems

**DOI:**http://doi.org/10.5455/jjee.204-1654826074