Stability analysis of distributed design systems using sum of squares programming
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This thesis provides a framework based on sum of squares (SOS) programming to study the stability of nonlinear polynomial dynamic systems. An algorithmic approach to analyzing stability using Lyapunov functions is the key contribution of this thesis. Several techniques and algorithms for stability analysis and controller synthesis are presented. The main application area investigated here is that of distributed design systems. The focus here is on studying the convergence properties of the solution process of decentralized or distributed subsystems, where each subsystem has its own design problem, including objective(s), constraints, and design variables. The challenging aspect of this type of problem comes in the coupling of the subsystems, which create complex research and implementation challenges in modeling and solving these types of problems. In this work, the domain of attraction, or region where convergence to a stable equilibrium point is guaranteed, of a decentralized design process is studied. The results demonstrate the advantage of using the methods described to get improved solutions over previously existing ones.