Stability analysis of a combined direct variable structure adaptive control – the discrete‐time case

This paper presents the proofs of robust stability of a discrete‐time robust model reference controller combined with variable structure in an adaptive framework. All the proofs of robust stability are derived for the discrete‐time case and are similar to those already existing for the conventional non‐combined case. The controller is applied to a SISO LTI plant with unmodeled dynamics of multiplicative and additive types. It is shown that the combined controller can arbitrarily improve the convergence of the error while maintaining the robustness if compared with the non–combined case. Simulation results illustrate the performance of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.