Abstract This paper is concerned with the stabilization and optimal control of discrete-time systems with multiplicative noise and multiple input delays. First, it is shown that the systems are stabilizable if and only if some algebraic Riccati-type equations have a solution which satisfies a given condition. To the best of our knowledge, this is the first time to propose a necessary and sufficient stabilizing condition for general multiple-input delay systems with multiplicative noise. The method constructs a Lyapunov–Krasovskii function based on the optimal cost of a finite-horizon LQR problem. Next, under the assumption that the system is stabilizable, an infinite-horizon LQR problem is investigated. The optimal control and the optimal cost are given by the above algebraic Riccati-type equations. Finally, based on the above stabilizing condition, an exact delay range for the stabilization of the system is derived in a special case.

中文翻译：

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具有乘性噪声和多输入延迟的离散时间系统的稳定和优化控制

摘要 本文涉及具有乘性噪声和多输入延迟的离散时间系统的稳定和优化控制。首先，证明了当且仅当某些代数 Riccati 型方程具有满足给定条件的解时，系统才是稳定的。据我们所知，这是第一次为具有乘法噪声的一般多输入延迟系统提出充分必要的稳定条件。该方法基于有限范围 LQR 问题的最优成本构造 Lyapunov-Krasovskii 函数。接下来，在系统可稳定的假设下，研究了一个无限视距 LQR 问题。最优控制和最优成本由上述代数 Riccati 型方程给出。最后，