An approach to output feedback control for hybrid discrete-time systems subject to uncertain mode transitions is proposed. The system dynamics may assume different modes upon the occurrence of a switching that is not directly measurable. Since the current system mode is unknown, a regulation scheme is proposed by combining a Luenberger observer to estimate the continuous state, a mode estimator, and a controller fed with the estimates of both continuous state variables and mode. The closed-loop stability is ensured under suitable conditions given in terms of linear matrix inequalities. Since complexity and conservativeness grow with the increase of the modes, we address the problem of reducing the number of linear matrix inequalities by providing more easily tractable stability conditions. Such conditions are extended to deal with systems having also Lipschitz nonlinearities and affected by disturbances. The effectiveness of the proposed approach is shown by means of simulations.

中文翻译：

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一类混合线性和非线性系统的基于观测器的控制

提出了一种基于不确定模式转变的混合离散时间系统的输出反馈控制方法。发生不可直接测量的切换时，系统动力学可能会采用不同的模式。由于当前的系统模式未知，因此提出了一种调节方案，方法是将Luenberger观测器组合以估计连续状态，模式估计器和控制器，控制器提供连续状态变量和模式的估计值。在根据线性矩阵不等式给出的合适条件下，可以确保闭环稳定性。由于复杂度和保守度随模数的增加而增长，因此我们通过提供更易于处理的稳定性条件来解决减少线性矩阵不等式数量的问题。这样的条件扩展到也具有Lipschitz非线性并且受干扰影响的系统。仿真表明了所提方法的有效性。