## Trace bounds on the solution of the algebraic matrix Riccati and Lyapunov equation.(English)Zbl 0616.15013

The upper and lower bounds on the trace of the solutions of the algebraic Riccati equation and the Lyapunov equation are derived. The tightness of the upper bound is demonstrated by an example. The results may be applied to the design of a suboptimal feedback law and its corresponding cost can be estimated by these bounds.
Reviewer: H.D.Fischer

### MSC:

 15A24 Matrix equations and identities 15A42 Inequalities involving eigenvalues and eigenvectors 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93E11 Filtering in stochastic control theory 93C35 Multivariable systems, multidimensional control systems
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