## Abstract

In this paper we develop a H∞-type theory, from the dissipation point of view, for a large class of time-continuous stochastic nonlinear systems. In particular, we introduce the notion of stochastic dissipative systems analogously to the familiar notion of dissipation associated with deterministic systems and utilize it as a basis for the development of our theory. Having discussed certain properties of stochastic dissipative systems, we consider time-varying nonlinear systems for which we establish a connection between what is called the L2-gain property and the solution to a certain Hamilton-Jacobi inequality (HJI), that may be viewed as a bounded real lemma for stochastic nonlinear systems. The time-invariant case with infinite horizon is also considered, where for this case we synthesize a worst case-based stabilizing controller. Stability in this case is taken to be in the mean-square sense. In the stationary case, the problem of robust state feedback control is considered in the case of norm-bounded uncertainties. A solution is then derived in terms of linear matrix inequalities.

Original language | English |
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Pages (from-to) | 247-257 |

Number of pages | 11 |

Journal | Systems and Control Letters |

Volume | 55 |

Issue number | 3 |

DOIs | |

State | Published - 1 Mar 2006 |

## Keywords

- Disturbance attenuation
- H-infinity
- Linear matrix inequalities
- Nonlinear systems
- Stochastic systems

## ASJC Scopus subject areas

- Control and Systems Engineering
- General Computer Science
- Mechanical Engineering
- Electrical and Electronic Engineering

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