Nonlinear Synthesis : Proceedings of a IIASA Workshop held in Sopron Hungary June 1989 In its broadest sense nonlinear synthesis involves in fact the synthesis of sometimes so­ phisticated or complex control strategies with the aim of prescribing or at least influencing the evolution of complex nonlinear systems. Nonlinear synthesis requires the development of methodologies for modeling complex systems for the analysis of nonlinear models and for the systematic design of control schemes or feedback laws which can achieve a wide variety of prescribed objectives. The modeling analysis and control of complex systems in the face of uncertainty form on of the major components of the current research program in the Department of Systems and Decision Sciences (SDS) at the International Institute for Applied Systems Analysis (IIASA). In June 1989 a IIASA workshop on Nonlinear Synthesis sponsored by SDS was held in Sopron Hungary. We are proud to present this volume as the proceedings of this workshop a workshop attened by prominent researchers in nonlinear systems from both the East and the West. Since the promotion and encouragement of scientific cooperation between researchers in the East and in the West is one of the goals at IIASA we feel the Sopron Conference on Nonlinear Synthesis was very successful. Moreover we were especially pleased by the impressive new advances presented at the workshop which in this volume are now part of the conference record. Morse Theory and Optimal Control Problems Viability Kernel of Control Systems New Methods for Shaping the Response of a Nonlinear System Asymptotic Stabilization of Low Dimensional Systems Zero Dynamics in Robotic Systems Adaptive Methods for Piecewise Linear Filtering Nonlinear Feedback Control for Flexible Robot Arms Methods of Nonlinear Discontinuous Stabilization Invariant Manifolds Zero Dynamics and Stability Tracking Control for Robotic Manipulators by Local Linear Feedback Synthesis of Control Systems Under Uncertainty Conditions (Game Theory) Ellipsoidal Techniques for the Problem of Control Synthesis Extened Gaussian Quadrature and the Identification of Linear Systems Multirate Sampling and Zero Dynamics: from Linear to Nonlinear Factorization of Nonlinear Systems On the Approximation of Set Valued Mappings in a Uniform (Chebyshev) Metric Estimation of a Guaranteed Result in Nonlinear Differential Games of Encounter Limit Sets of Trajectories Nonlinear Systems with Impulsive and Generalized Function Controls Extremal Trajectories Small time Reachable Sets and Local Feedback Synthesis: A Synopsis of the Three dimensional Case Regularity Properties of the Minimum time Map Optimal Synthesis Containing Chattering Arcs and Singular Arcs of the Second Order The Invariants of Optimal Synthesis Author’s Index.