Matrix Exponential and Control- Part I: Derivation and Connection with State Equations
#controltheory #controlengineering #robotics #controleducation #roboticseducation #automation #mechatronics #lyapunov #numerics #linearalgebra #signalprocessing #machinelearning #reinforcementlearning
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In this control engineering and control theory tutorial, we explain how to define the matrix exponential. We explain that the definition of the matrix exponential originates from the solution of the state-space equation of a linear dynamical system. The definition of the matrix exponential is based on the matrix power series expansion. We also explain what is a resolvent matrix. In the next video tutorial, we explain how to compute the matrix exponential by using the inverse Laplace transform. We also explain that the matrix exponential is essentially the state transition matrix of a dynamical system.