Mathematics and Computers in Simulation 63 (2003) 15–34 Robust adaptive stabilizer of a class of time-varying plants using multiple controllers S. Alonso-Quesada ∗ , M. de la Sen Processes Research and Development Institute, IIDP, Electricity and Electronics Department, Faculty of Sciences of the Basque Country University, Leioa (Bizkaia), B.P. 644, 48080 Bilbao, Spain Received 1 August 2002; accepted 4 October 2002 Abstract This paper presents an indirect adaptive control scheme for nominally stabilizable, non-necessarily inversely stable, first-order continuous-time systems with unmodeled dynamics. The control objective is the adaptive stabi- lization of the closed-loop system with a bounded tracking error between the system output and a reference signal given by a stable filter. The adaptive control scheme includes several estimation algorithms and a supervisor to select the appropriate estimator at certain time instants while keeping it in operation during at least a minimum residence or dwell time. Such selection is based on a criterion relative to the estimation errors obtained with each estimator. All estimators are of either least square or gradient type. The estimators include relative dead-zones for robustness purposes and parameter ‘a posteriori’ modifications to ensure the controllability of the estimated models of the plant. This is crucial to prove the stabilizability of the plant via adaptive pole-placement designs. The multi-estimation scheme renders the overall system highly nonlinear. © 2002 IMACS. Published by Elsevier Science B.V. All rights reserved. Keywords: Adaptive control; Multi-estimation; Robustness; Stability analysis; Time-varying plants 1. Introduction Adaptive control theory has developed significantly during the last few decades [11,16]. Initially, the design of adaptive controllers for stabilization of unknown linear time-invariant plants was con- sidered [10,18]. This study was later extended to stabilization of unknown linear time-varying plants. Particularly, the design of control systems based on multi-estimation techniques has been developed by Morse [15] and Narendra and Balakrishnan [17] for stabilization of plants whose parameters are unknown piecewise constant and bounded functions. In [15] a supervisory system with a set of fixed controllers is designed for tracking of a reference signal. The supervisor switches from one controller ∗ Corresponding author. Tel.: +34-4-6015-311; fax: +34-4-6013-071. E-mail address: santi@we.lc.ehu.es (S. Alonso-Quesada). 0378-4754/02/$ – see front matter © 2002 IMACS. Published by Elsevier Science B.V. All rights reserved. PII:S0378-4754(02)00207-0