Global least squares solution for LTI system response

Linear time invariant (LTI) systems are the most important method to describe dynamic systems for the purpose of modeling, simulation and design of controllers. Dynamic systems are a process developing over time, hence the solution is an initial value problem (IVP). Solvers for ordinary differential equations (ODE) are commonly used for evaluation. A new idea is to solve such systems directly after discretization based on an least-squares problem with equality constraints (LSE). The approach is demonstrated on a simple system with four state variables and a rank-deficient system matrix. A comparison with standard ODE solution shows the correctness of the solution, advantages are discussed.