This paper considers the problems of stability and filtering for a class of linear hybrid systems with nonlinear uncertainties and Markovian jump parameters. The hybrid system under study involves a continuous-valued system state vector and a discretevalued system mode. The unknown nonlinearities in the system are time varying and norm bounded. The Markovian jump parameters are modeled by a Markov process with a finite number of states. First, we show the equivalence of the sets of norm-bounded linear and nonlinear uncertainties. Then, instead of the original hybrid linear system with nonlinear uncertainties, we consider the same system with linear uncertainties. By using a Riccati equation approach for this new system, a robust filter is designed using two sets of coupled Riccati-like equations such that the estimation error is guaranteed to have an upper bound. \ud
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机译:本文考虑了一类具有非线性不确定性和马尔可夫跳跃参数的线性混合系统的稳定性和滤波问题。所研究的混合系统涉及一个连续值系统状态向量和一个离散值系统模式。系统中未知的非线性是随时间变化的并且受范数限制。马尔可夫跳跃参数通过具有有限状态数的马尔可夫过程进行建模。首先,我们证明了范数有界的线性和非线性不确定性的等价性。然后,代替具有非线性不确定性的原始混合线性系统,我们考虑具有线性不确定性的相同系统。通过针对该新系统使用Riccati方程方法,使用两组耦合的Riccati式方程设计了鲁棒滤波器,从而确保了估计误差的上限。 \ ud
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