## New results for the bounds of the solution for the continuous Riccati and Lyapunov equations.(English)Zbl 0867.93038

The paper provides upper and lower estimates for the matrix solution $$P$$ of the continuous algebraic matrix Riccati equation $$A^{T} P + P A - P R P = -Q$$. Moreover, a lower matrix bound for the solution $$P$$ of the continuous Lyapunov equation $$A^{T} P + P A = -Q$$ is also obtained. By these bounds, the estimates of each eigenvalue including extreme ones, the trace, and the determinant of $$P$$ are given. Three comparisons between the present results and those already known are reported. This shows that some bounds are sharper than those found so far. Finally, an illustrative example is provided.

### MSC:

 93C05 Linear systems in control theory 15A24 Matrix equations and identities 93C99 Model systems in control theory
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