This paper presents a method for data-driven analysis and control of continuous-time systems using orthogonal polynomial bases (POBs). The approach involves transforming continuous-time input and state trajectories into discrete sequences of coefficients from their POB representations. This transformation allows the dynamics of the transformed signals to be described by the same system matrices as the original continuous-time trajectories. The method is applied to solve informativity, quadratic stabilization, and H₂-performance problems for continuous-time systems. The paper shows that POBs provide a powerful tool for data-driven control, as they allow for accurate and efficient computation of signal representations, and enable the derivation of system matrices directly from data. The method is particularly effective when machine-precision accuracy can be achieved from the data using a finite number of basis elements. The paper also addresses the case where approximation errors are non-negligible, and shows how to use the matrix S-lemma to solve quadratic stabilization and H₂-performance problems in such cases. The results demonstrate that POBs offer a data-driven framework for control of continuous-time systems, with minimal assumptions about the system dynamics. The paper also discusses the use of POBs for system identification, controllability, and state feedback stabilization, and provides examples to illustrate the method. The results show that POBs can be used to derive system matrices directly from data, and that the method is effective for both noiseless and noisy data scenarios. The paper concludes that POBs provide a valuable tool for data-driven analysis and control of continuous-time systems.This paper presents a method for data-driven analysis and control of continuous-time systems using orthogonal polynomial bases (POBs). The approach involves transforming continuous-time input and state trajectories into discrete sequences of coefficients from their POB representations. This transformation allows the dynamics of the transformed signals to be described by the same system matrices as the original continuous-time trajectories. The method is applied to solve informativity, quadratic stabilization, and H₂-performance problems for continuous-time systems. The paper shows that POBs provide a powerful tool for data-driven control, as they allow for accurate and efficient computation of signal representations, and enable the derivation of system matrices directly from data. The method is particularly effective when machine-precision accuracy can be achieved from the data using a finite number of basis elements. The paper also addresses the case where approximation errors are non-negligible, and shows how to use the matrix S-lemma to solve quadratic stabilization and H₂-performance problems in such cases. The results demonstrate that POBs offer a data-driven framework for control of continuous-time systems, with minimal assumptions about the system dynamics. The paper also discusses the use of POBs for system identification, controllability, and state feedback stabilization, and provides examples to illustrate the method. The results show that POBs can be used to derive system matrices directly from data, and that the method is effective for both noiseless and noisy data scenarios. The paper concludes that POBs provide a valuable tool for data-driven analysis and control of continuous-time systems.