## Advances in Statistical Control, Algebraic Systems Theory, and Dynamic Systems Characteristics: A Tribute to Michael K. SainChang-Hee Won, Cheryl B. Schrader, Anthony N. Michel Life has many surprises. One of the best surprises is meeting a caring mentor, an encouraging collaborator, or an enthusiastic friend. This volume is a tribute to P- fessor Michael K. Sain, who is such a teacher,colleague,and friend.On the beautiful fall day of October 27, 2007, friends, families, colleagues, and former students ga- ered at a workshop held in Notre Dame, Indiana. This workshop brought together many people whose lives have been touched by Mike to celebrate his milestone 70th birthday, and to congratulate him on his contributions in the elds of systems, c- cuits, and control. Mike was born on March 22, 1937, in St. Louis, Missouri. After obtaining his B.S.E.E. and M.S.E.E. at St. Louis University, he went on to study at the University of Illinois at Urbana-Champaignfor his doctoral degree. With his Ph.D. degree c- plete, he came to the University of Notre Dame in 1965 as an assistant professor. He became an associate professor in 1968, a full professor in 1972, and the Frank M. Freimann Chair in Electrical Engineering in 1982. He has remained at and loved the University of Notre Dame for over 40 years. Mike also held a number of consu- ing jobs throughout his career. Most notably, he consulted with the Energy Controls Division of Allied-Bendix Aerospace from 1976 to 1988 and the North American Operations branch of the Research and Development Laboratory of General Motors Corporation for a decade, 1984–1994. |

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### Contents

Going Beyond the Mean | 3 |

The CostVariance DiscreteTime Case | 29 |

Performance Robustness Analysis | 43 |

MultiCumulant and Pareto Solutions for Tactics Change Prediction and Performance Analysis in Stochastic MultiTeam Noncooperative Games | 65 |

A Multiobjective Cumulant Control Problem | 99 |

Realization and Decoupling | 129 |

Modules of Zeros for Linear Multivariable Systems | 145 |

Zeros in Linear TimeDelay Systems | 159 |

Characterization and Calculation of Approximate Decentralized Fixed Modes ADFMs | 223 |

Some New Nonlinear and Symbol Manipulation Techniques to Mitigate Adverse Effects of High PAPR in OFDM Wireless Communications | 245 |

Homogeneous Domination and the Decentralized Control Problem for Nonlinear System Stabilization | 257 |

Volterra Control Synthesis | 281 |

Master of Engineering? | 313 |

A Conversation in Two Languages | 319 |

Publications of Michael K Sain | 331 |

357 | |

On the Status of the Stability Theory of Discontinuous Dynamical Systems | 173 |

Biologically Inspired Feedback Control | 201 |

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ADFMs Algebraic Systems Theory algorithm American Control Conference approach Assumption asymptotic stability Automatic Control B.F. Wyman Benchmark continuous-time control problem control systems cost cumulants cost function cost variance Cumulant Control Dame decentralized control decision defined Definition denoted differential equation discrete-time dynamical systems dynamic programming exists feedback controller finite fixed modes given homogeneous IEEE IEEE Transactions input inverse K. D. Pham Kalman Lemma linear system Lyapunov function Lyapunov stability M. K. Sain matrix MCV control method Michael Michael K minimize Multivariable Nash equilibrium nonlinear systems OFDM optimal control output feedback stabilization PAPR reduction performance index performance measure policy iteration polynomial Proceedings Proof quadratic realization recursion Risk-Sensitive S. R. Liberty satisfies Section semimodule semiring space Springer Science+Business Media statistical control stochastic strategy structure sub-semimodule Systems Theory techniques Theorem tion to,tf transfer function Variance Control Volterra zero module