Filtering and Control of Stochastic Jump Hybrid Systems by Xiuming Yao Ligang Wu & Wei Xing Zheng

Author:Xiuming Yao, Ligang Wu & Wei Xing Zheng
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

7.2 Problem Statement and Preliminaries

Fix a probability space , where is the sample space, is the -algebra of subsets of the sample space and is the probability measure on . Under this probability space, we consider the following MJLs with nonlinearity:

(7.1)

where is the state vector, is the control input, are nonlinear vector functions, is supposed to satisfy bounded conditions described as Assumption 7.1, which can represent the constant and harmonic noises. is another disturbance which is assumed to be an arbitrary signal in . is a continuous-time Markov process with right continuous trajectories and taking values in a finite set with transition probability matrix given by (2.​2).

Assumption 7.1

The disturbance in the control input path can be formulated by the following exogenous system

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