This work presents a novel method to solve analysis and design problems for nonlinear control systems, the classical solutions of which rely on the solvability, or on the solution itself, of partial differential equations or inequalities. The first part of the thesis is dedicated to the analysis of nonlinear systems. The notion of Dynamic Lyapunov function is introduced. These functions allow to study stability properties of equilibrium points, similarly to standard Lyapunov functions. In the

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... rmer, however, a positive definite function is combined with a dynamical system that render Dynamic Lyapunov functions easier to construct than Lyapunov functions. These ideas are then extended to characterize Dynamic Controllability and Observability functions, which are exploited in the model reduction problem for nonlinear systems. Constructive solutions to the L2-disturbance attenuation and the optimal control problems are proposed in the second part of the thesis. The key aspect of these solutions is the definition of Dynamic Value functions that, generalizing Dynamic Lyapunov functions, consist of a dynamical feedback and a positive definite function. In the last part of the thesis a similar approach is utilized to simplify the observer design problem via the Immersion and Invariance technique. Finally, the effectiveness of the methodologies is illustrated by means of several applications, including range estimation and the optimal robust control of mechanical systems, combustion engine test benches and the air path of a diesel engine.