In this chapter, it is the objective to deal with the mixed H2/H∞ control problem for a class of stochastic time‐varying systems with nonlinearities. The nonlinearities are described by statistical means and could cover several kinds of well‐studied nonlinearities as special cases. The occurrence of the addressed nonlinearities is governed by two sequences of Bernoulli distributed white sequences with known probabilities. Such nonlinearities are named as randomly occurring nonlinearities (RONs) as they appear in a probabilistic way. The purpose of the problem under investigation is to design a controller such that the closed‐loop system achieves the pre‐specified H∞ disturbance attenuation level and, at the same time, the energy of system output is minimized when the worst‐case disturbance happens. A sufficient condition is given for the existence of the desired controller by means of the solvability of certain coupled matrix equations. By resorting to the game theory approach, an algorithm is developed to obtain the controller gain at each sampling instant.


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    Title :

    Mixed H2/H∞ Control with Randomly Occurring Nonlinearities: The Finite‐Horizon Case


    Contributors:
    Ma, Lifeng (author) / Wang, Zidong (author) / Bo, Yuming (author)


    Publication date :

    2015-03-16


    Size :

    16 pages




    Type of media :

    Article/Chapter (Book)


    Type of material :

    Electronic Resource


    Language :

    English