Solutions of differential-algebraic equations as outputs of LTI systems: application to LQ control problem

2013/12/29 by Mihály Petreczky, Petreczky, Mihaly, Sergiy Zhuk +1
Computer Science · Engineering · Mathematics · #Control and Stability of Dynamical Systems #FOS: Mathematics #Modeling and Simulation Systems #Numerical methods for differential equations #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1312.7547

openalex publication_date 2013/12/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we synthesize behavioral ideas with geometric control theory and propose a unified geometric framework for representing all solutions of a Linear Time Invariant Differential-Algebraic Equation (DAE-LTI) as outputs of classical Linear Time Invariant systems (ODE-LTI). An algorithm for computing an ODE-LTI that generates solutions of a given DAE-LTI is described. It is shown that two different ODE-LTIs which represent the same DAE-LTI are feedback equivalent. The proposed framework is then used to solve an LQ optimal control problem for DAE-LTIs with rectangular matrices.

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