一类不确定混合线性时滞系统鲁棒控制问题研究

讨论了一类不确定混合线性时滞系统在其Markov跳跃参数所处模态非精确可测得情况下的鲁棒控制问题。给出了非匹配条件下系统不确定部分范数上界已知时,使系统呈均方意义下指数稳定的保代价控制充分条件。并根据混合系统模式下的LaSalle稳定性定理,对匹配条件下系统不确定部分的未知范数上界给出了一种参数自适应估计方法,设计了相应的鲁棒自适应控制律以实现混合线性时滞系统以概率1渐近稳定。鲁棒自适应控制律的设计仅依赖于跳跃参数的非精确测量值。

Research of robust control for a class of time-delayed uncertain hybrid linear systems

The robust control problems for a class of time()-delayed uncertain linear systems with Markovian jumping parameters are discussed.Firstly,under the assumption of complete knowledge of the norm bounds of the system uncertainties,sufficient conditions which guarantee the bounds of the given performance index and the exponential stability in mean square of the uncertain systems are given.Secondly,according to Markovian jumping versions of LaSalle stability theorem,a robust parameter adaptive control strategy is proposed,which guarantees the asymptotic stability of the matched-uncertain jump systems with probability one.A key feature of this scheme is that the controller design only depends on the inaccurate measurement of the jumping parameter,and the prior knowledge of the norm upper bounds of the system uncertainties is not required.