In this note, constant reference tracking using integral control for negative-imaginary (NI) systems preceded by hysteresis nonlinearity is addressed. The hysteresis nonlinearity is considered to be slope-restricted, though no specific modeling framework is exploited. It is effectively shown that integral tracking controllers are guaranteed to exist when a stable NI system with sign-definite dc-gain is preceded by such hysteresis nonlinearities. When the dc-gain is negative-definite, under positive feedback configuration with positive slope-restricted hysteresis, it is established that the integral controller gain can be any positive diagonal matrix. The development of the proposed model-independent inversion-free scheme is carried out in general state-space setting and is applicable for multiple-input multiple-output systems with decoupled hysteresis nonlinearities. Effectiveness of the results is illustrated with examples.

中文翻译：

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滞后非线性之前的稳定负虚系统的积分控制

在本说明中，针对滞后非线性之前的负虚数 (NI) 系统使用积分控制的恒定参考跟踪得到解决。尽管没有利用特定的建模框架，但滞后非线性被认为是斜率限制的。有效地表明，当具有符号确定的直流增益的稳定 NI 系统之前存在这种滞后非线性时，可以保证存在积分跟踪控制器。当直流增益为负定时，在正反馈配置下具有正斜率限制滞后，积分控制器增益可以是任何正对角矩阵。所提出的与模型无关的无反演方案的开发在一般状态空间设置中进行，适用于具有解耦滞后非线性的多输入多输出系统。结果的有效性用例子来说明。