## Optimal Control, Stabilization and Nonsmooth AnalysisMarcio S. de Queiroz, Michael Malisoff, Peter Wolenski This edited book contains selected papers presented at the Louisiana Conference on Mathematical Control Theory (MCT'03), which brought together over 35 prominent world experts in mathematical control theory and its applications. The book forms a well-integrated exploration of those areas of mathematical control theory in which nonsmooth analysis is having a major impact. These include necessary and sufficient conditions in optimal control, Lyapunov characterizations of stability, input-to-state stability, the construction of feedback mechanisms, viscosity solutions of Hamilton-Jacobi equations, invariance, approximation theory, impulsive systems, computational issues for nonlinear systems, and other topics of interest to mathematicians and control engineers. The book has a strong interdisciplinary component and was designed to facilitate the interaction between leading mathematical experts in nonsmooth analysis and engineers who are increasingly using nonsmooth analytic tools. |

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### Contents

Is the Stability Robust? | 3 |

On the Interpretation of Nonanticipative Control Strategies in Differential Games and Applications to Flow Control | 29 |

Nonuniqueness in Systems of HamiltonJacobi Equations | 49 |

On Impulses Induced by Singular Perturbations | 61 |

Optimal Control of DifferentialAlgebraic Inclusions | 73 |

The Singular Case | 85 |

MinPlus Eigenvector Methods for Nonlinear H Problems with Active Control | 101 |

Optimization and Feedback Control of Constrained Parabolic Systems under Uncertain Perturbations | 121 |

Quantitative Aspects of the InputtoStateStability Property | 215 |

Explicit Formulae for Boundary Control of Parabolic PDEs | 231 |

A Continuous Control Mechanism for Uncertain Nonlinear Systems | 251 |

Nonsmooth Analysis and Applications | 265 |

Lyapunov Functions and Feedback in Nonlinear Control | 267 |

Local Problems | 283 |

Deformations and Flows | 299 |

Uniqueness and Duality of Solutions | 313 |

Stabilization and Lyapunov Functions | 133 |

Interconnections of Monotone Systems with SteadyState Characteristics | 135 |

The Effect of Actuator Errors | 155 |

AGAS and SRS Feedbacks | 173 |

Stabilization by Patchy Feedbacks and Robustness Properties | 185 |

A SmallGain Viewpoint | 201 |

Smooth and Nonsmooth Duality for Free Time Problems | 323 |

One Sided Lipschitz Multifunctions and Applications | 333 |

A Characterization of Strong Invariance for Perturbed Dissipative Systems | 343 |

Generalized Differentiation for Moving Objects | 351 |