### Abstract

This paper introduces the definition of the nonstandard linear discrete-time singularly perturbed system and then shows how to solve the corresponding linear-quadratic optimal control problem since the methodology that exists in the literature for the solution of the standard singularly perturbed discrete linear-quadratic optimal control problem can not be extended to the corresponding nonstandard counterpart. The solution of the optimal control problem is obtained in terms of the pure-slow and pure-fast, reduced-order, continuous-time, algebraic Riccati equations. An example is included to illustrate the efficiency of the proposed method.

Original language | English |
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Pages (from-to) | 163-174 |

Number of pages | 12 |

Journal | Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm |

Volume | 9 |

Issue number | 2 |

Publication status | Published - 2002 Jun 1 |

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### Keywords

- Optimal control
- Order reduction
- Parallel computation
- Riccati equation
- Singular perturbation

### ASJC Scopus subject areas

- Applied Mathematics
- Discrete Mathematics and Combinatorics