Stability Analysis and Stabilization of Randomly Switched Systems
Stability Analysis and Stabilization of Randomly Switched Systems
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DOI：
10.1109/cdc.2006.377668
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发表时间：
2006-12
期刊：
影响因子：
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通讯作者：
Debasish Chatterjee;D. Liberzon
中科院分区：
文献类型：
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作者：
Debasish Chatterjee;D. Liberzon
本文研究具有控制输入的随机切换系统的稳定性分析和镇定问题。切换信号被建模为与系统状态无关的跳跃随机过程；它在每个时刻从一族确定性系统中选择活动的子系统。考虑了三种不同类型的切换信号：第一种是满足统计慢切换条件的跳跃随机过程，第二种和第三种是跳跃随机过程，它们在跳跃时刻具有独立同分布的值，并且具有指数保持时间和均匀保持时间。对于这三种情况，我们首先建立了当子系统不具有控制输入时切换系统随机稳定的充分条件；在后两种情况下，并不要求每个子系统都是稳定的。然后，当控制中的子系统是仿射的并且不是所有的零输入稳定时，我们设计反馈控制器，控制空间是ROPFM的一般子集。我们的分析结果和相应控制空间下的非线性系统反馈镇定的普遍公式构成了控制设计的主要工具
This article is concerned with stability analysis and stabilization of randomly switched systems with control inputs. The switching signal is modeled as a jump stochastic process independent of the system state; it selects, at each instant of time, the active subsystem from a family of deterministic systems. Three different types of switching signals are considered: the first is a jump stochastic process that satisfies a statistically slow switching condition; the second and the third are jump stochastic processes with independent identically distributed values at jump times together with exponential and uniform holding times, respectively. For each of the three cases we first establish sufficient conditions for stochastic stability of the switched system when the subsystems do not possess control inputs; not every subsystem is required to be stable in the latter two cases. Thereafter we design feedback controllers when the subsystems are affine in control and are not all zero-input stable, with the control space being general subsets of Ropfm. Our analysis results and universal formulae for feedback stabilization of nonlinear systems for the corresponding control spaces constitute the primary tools for control design