Bounds for the eigenvalues of the continuous algebraic Riccati equation

@article{Liu2011BoundsFT,
  title={Bounds for the eigenvalues of the continuous algebraic Riccati equation},
  author={Jianzhou Liu and Juan Zhang},
  journal={Int. J. Systems Science},
  year={2011},
  volume={42},
  pages={1747-1753}
}
where x02R is the initial state of the system and K is the positive definite solution of the CARE (1). An interpretation of tr(K ) is that tr(K )/n is the average value of the cost (2) as x0 varies over the surface of a unit sphere. As we all know, for one thing, the analytical solution of this equation is often computationally difficult and time-consuming as the dimensions of the system matrices increase. For another, we can only solve some special Riccati matrix equations and design… CONTINUE READING

From This Paper

Topics from this paper.

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 18 references

Diverse Bounds for the Eigenvalues of the Continues Algebraic Riccati Equation

  • N. Komaroff
  • IEEE Transactions on Automatic Control,
  • 1994
Highly Influential
17 Excerpts

On the Upper and Lower Bounds of the Solution for the Continuous Riccati Matrix Equation

  • C. H. Lee
  • International Journal of Control,
  • 1997
Highly Influential
13 Excerpts

Bounds on Eigenvalues of Matrix Products with an Application to the Algebraic Riccati Equation

  • N. Komaroff
  • IEEE Transactions on Automatic Control,
  • 1990
Highly Influential
15 Excerpts

A Matrix Inequality Associated with Bounds on Solutions of Algebraic Riccati and Lyapunov Equations

  • J. M. Saniuk, I. B. Rhodes
  • IEEE Transactions on Automatic Control,
  • 1987
Highly Influential
13 Excerpts

A Note on Eigenvalue Bounds in Algebraic Riccati Equation

  • V. R. Karanam
  • IEEE Transactions on Automatic Control,
  • 1983
Highly Influential
15 Excerpts

Upper and Lower Bounds on the Solution of Algebraic Riccati Equation

  • K. Yasuda, K. Hirai
  • IEEE Transactions on Automatic Control,
  • 1979
Highly Influential
13 Excerpts

Iterative Methods for the Extremal Positive Definite Solution of the Matrix Equation XþA X A1⁄4Q

  • Peng, Z.-Y, S. M. El-Sayed, Zhang, X.-L
  • Journal of Computational and Applied Mathematics,
  • 2007

On the Positive Definite Solutions of the Nonlinear Matrix Equation XþA X A1⁄4Q

  • V. I. Hasonov, S. M. El-Sayed
  • Linear Algebra and its Applications,
  • 2006
1 Excerpt

‘ On the Positive Definite Solutions of the Nonlinear Matrix Equation X þ A X   A 1⁄4 Q ’ , Linear Algebra and its Applications

  • V. I. Hasonov, S. M. El-Sayed
  • 2006
1 Excerpt

Bounds on Solutions of Algebraic Riccati and Lyapunov Equations: A Survey and New Results

  • W. H. Kwon, Y. S. Moon, S. C. Ahn
  • International Journal of Control,
  • 1996
1 Excerpt

Similar Papers

Loading similar papers…