A design method of discrete-time adaptive control systems based on immersion and invariance

Adaptive control systems are designed to achieve desired control performance when plant parameters gains are unknown, or possibly slowly changing. Highly calculation technology is developed, more important discrete-time adaptive control structure is. Because the relative degree condition for strict positive realness (SPR) of the discrete-time error transfer function is different from the condition of the continuous time case, it is hard to prove the stability of the discretized continuous-time adaptive control systems. The main contribution of this paper is the extension of an immersion and invariance (I&I)-based adaptive control algorithm from continuous to discrete time. The theoretical stability of the proposed discrete time I&I-based adaptive control system is proved. In order to show the effectiveness of the proposed method, numerical simulations are shown.