This paper describes some important classes of two degrees of freedom of underactuated mechanical system and also surveys review of the recent state-of-the-art concerning the mathematical modeling of these systems, their classification, and all the control strategies (linear, nonlinear, and intelligent) that have been made so far (i.e., from the year 2000 to date) to control these systems. Future research and challenges concerning the improvement, the effectiveness, and robustness of the proposed controllers for underactuated mechanical systems are presented.

Summary This paper is concerned with the delay‐dependent exponential stability analysis of two‐dimensional (2D) discrete switched systems with state delays described by the Roesser model; the delays under consideration are varying. By constructing an appropriate Lyapunov‐Krasovskii functional and using the average dwell time approach, new delay‐dependent sufficient conditions for the exponential stability of the system under study are proposed. In order to obtain less conservative conditions, the delay partitioning method is adopted as well as the free‐weighting matrix technique. The proposed conditions are formulated in the format of linear matrix inequality. The effectiveness and the reduced conservatism of the developed results are shown by illustrative examples.

This paper is concerned with the problem of robust stability of uncertain two-dimensional (2-D) discrete systems described by the Roesser model with polytopic uncertain parameters. Based on a newly developed parameter-dependent Lyapunov-Krasovski functional combined with Finsler's lemma, new sufficient conditions for robust stability analysis are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the effectiveness and less conservatism of the proposed results.

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The design of delay-dependent robust H∞ controllers is solved here for a class of uncertain 2-D continuous systems: those with interval time-varying delays and norm-bounded parameter uncertainties. By constructing a novel augmented Lyapunov-Krasovskii functional and then using the Wirtinger inequality, a new delay-dependent stability condition is developed, that uses the known lower and upper bounds of the time-varying delays to develop less conservative solutions that previous results in the literature. This condition is then applied to H∞ performance analysis and robust H∞ controller design, using linear matrix inequalities (LMIs).Two numerical examples are presented that illustrate the effectiveness of the proposed method.