Adaptive robust control for discrete-time systems with coprime factor perturbations

This paper presents an adaptive robust control scheme when a discrete-time plant is subjected to both coprime factor perturbations and unknown external disturbances. Firstly, we propose a recursive estimation for extended parameters in which includes the parameters of nominal model and the bound of perturbation factors and disturbances. Then, combining the recursive extended parameters estimation with l₁ optimal design we present a novel adaptive robust control scheme. With the help of the continuity properties of two-block l₁ optimization, the proposed adaptive algorithm is shown to be globally convergent. A posterior computable condition for the stability of the adaptive scheme is also provided. As compared with existed results, the controlled uncertainty plant considered in this paper is more typical, and the robust stability guarantee is non-conservation.