# Differential Algebra for Control Systems Design. Computation of Canonical Forms.

Title | Differential Algebra for Control Systems Design. Computation of Canonical Forms. |

Publication Type | Journal Article |

Year of Publication | 2013 |

Authors | Picó-Marco E |

Journal | Control Systems Magazine |

Volume | 33 |

Start Page | 52 |

Issue | 2 |

Pagination | 52 - 62 |

Abstract | Many systems can be represented using polynomial differential equations, particularly in process control, biotechnology, and systems biology [1], [2]. For example, models of chemical and biochemical reaction networks derived using the law of mass action have the form ẋ = Sv(k,x), (1) where x is a vector of concentrations, S is the stoichiometric matrix, and v is a vector of rate expressions formed by multivariate polynomials with real coefficients k . Furthermore, a model containing nonpolynomial nonlinearities can be approximated by such polynomial models as explained in "Model Approximation". The primary aims of differential algebra (DALG) are to study, compute, and structurally describe the solution of a system of polynomial differential equations,f (x,ẋ, ...,x |