### Abstract

In this paper two properties of minimum entropy control for linear time-varying systems are investigated. An entropy formulation for anti-causal systems is first considered. Minimizing the norm of an anticausal system is straightforward because of the fact that the norm of an operator is equal to the norm of its adjoint. This is not true for the entropy measure. For this reason a separate formula for the entropy of anti-causal systems is needed in order to consider dual problems that arise in optimal control theory. Secondly, we investigate the relationship between the entropy measure for time-varying systems and the H_{2} and H_{∞} norms. For time-invariant systems, minimum entropy control has been shown to be a good mixed H_{2}/H_{∞} controller. In this paper we show that this is also true in the time-varying case.

Original language | English (US) |
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Pages (from-to) | 341-347 |

Number of pages | 7 |

Journal | Systems and Control Letters |

Volume | 26 |

Issue number | 5 |

DOIs | |

State | Published - Dec 27 1995 |

### Keywords

- Discrete time
- Entropy
- H/H
- Operator norms
- Time varying

### ASJC Scopus subject areas

- Control and Systems Engineering
- Computer Science(all)
- Mechanical Engineering
- Electrical and Electronic Engineering