LAUSR

Output tracking control is currently receiving increased attention because of its applications in various fields [1–3]. Controller design for nonlinear systems with unstable linearization [4] is essential because such systems have several applications, including a class of underactuated mechanical systems. For the output tracking control for systems with unstable linearization, the global practical output tracking controller design was developed using the backstepping design method [5] and the asymptotic tracking control problem for a power-integrator planar system was addressed [6]. However, these studies did not consider quantization [5, 6]. However, signals are transmitted over communication channels and must therefore be quantized to model systems with quantization [7]. Unfortunately, a quantized tracking controller design for nonlinear systems with unstable linearizations has not been reported yet despite its potential in practical applications. This study provides a solution to address this problem. The two main contributions of this study are as follows. (1) This study is the first to present results on the quantized tracking control for nonlinear systems with unstable linearization. Quantization is inevitable and useful for control systems and quantization schemes that require a low communication rate; therefore, the results reported herein are more practical than the corresponding non-quantized control solutions [5, 6]. (2) This study considers systems with unstable linearization, including the linearizable nonlinear systems [7], as special cases. Because the Jacobian linearization of systems studied herein may have eigenvalues with positive real parts, some new techniques can be developed for the controller design and stability analysis. Problem formulation. This study aims to design controllers to obtain the output of the following system: