In this chapter, the robust variance-constrained *H*_{∞} control problem is investigated for a class of nonlinear stochastic systems with possible sensor failures that are occurring in a random way. Such a phenomenon is called randomly occurring sensor failures (ROSFs). The nonlinearities described by statistical means could cover several well-studied nonlinearities, and the occurrence of the sensor failures is governed by a Bernoulli distributed random variable. The purpose of the addressed problem is to design an output-feedback controller such that, for certain systems with ROSFs, (1) the closed-loop system meets the desired *H*_{∞} performance over a finite horizon and (2) the state covariance is not more than a pre-specified upper bound at each time point. A sufficient condition for the existence of the desired controller is given and a computing algorithm is developed to achieve the aforementioned requirements simultaneously by means of a recursive linear matrix inequalities (RLMIs) approach. An illustrative simulation example is provided to show the applicability of the proposed algorithm.

The rest of the chapter is arranged as follows: Section 13.1 formulates the control problem for the nonlinear stochastic systems with ROSFs. In Section 13.2, the *H*_{∞} and variance performance indices are firstly analyzed separately, and then a theorem is proposed to combine the two ...

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