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The paper provides new algorithms for analysis and design of nonlinear event-triggered control systems represented in some standard form that accommodates a continuous plant and a discrete dynamic controller. Discrete control signals are generated using uniformly sampled data of the plant output and updated whenever a specific event triggering condition is satisfied. It is shown that using the reduction method and sublinear vector Lyapunov functions, analysis problems of the considered event-triggered system can be reduced to similar problems for an auxiliary discrete one. Based on such reduction, we propose algorithms that provide: verification of various dynamic properties of the event-triggered system; estimation of main indicators of its dynamic quality (such as stabilization error, stability region, and settling time); synthesis of unknown parameters, including feedback gains and parameters of the event triggering condition, that ensure the optimal or desired quality of the system. Several test examples and an application to the formation control problem for a team of autonomous underwater vehicles are considered to validate the developed algorithms.