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首页> 外文期刊>SIAM Journal on Control and Optimization >Discrete-time and sampled-data low-gain control of infinite-dimensional linear systems in the presence of input hysteresis
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Discrete-time and sampled-data low-gain control of infinite-dimensional linear systems in the presence of input hysteresis

机译：输入滞回作用下的无穷维线性系统的离散时间和采样数据低增益控制

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摘要

We introduce a general class of causal dynamic discrete-time nonlinearities which have certain monotonicity and Lipschitz continuity properties. In particular, the discretizations of a large class of continuous-time hysteresis operators obtained by applying the standard sampling and hold operations belong to this class. It is shown that closing the loop around a power-stable, linear, infinite-dimensional, discrete-time, single-input, single-output system, subject to an input nonlinearity from the class under consideration and compensated by a discrete-time integral controller, guarantees asymptotic tracking of constant reference signals, provided that ( a) the positive integrator gain is sufficiently small and (b) the reference value is feasible in a very natural sense. We apply this result in the development of sampled-data low-gain integral control for exponentially stable, regular, linear, infinite-dimensional, continuous-time systems subject to input hysteresis. [References: 30]
机译：我们介绍了具有某些单调性和Lipschitz连续性的因果动态离散时间非线性的一般类。特别地，通过应用标准采样和保持操作获得的一大类连续时间磁滞算子的离散化属于此类。结果表明，围绕功率稳定的，线性，无限维，离散时间，单输入，单输出系统的闭合回路受所考虑类别的输入非线性的影响，并由离散时间积分补偿如果（a）正积分器增益足够小并且（b）参考值在非常自然的意义上是可行的，则控制器可以保证恒定参考信号的渐近跟踪。我们将此结果应用到采样数据低增益积分控制的开发中，该控制用于受输入滞后影响的指数稳定，规则，线性，无限维，连续时间系统。 [参考：30]

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