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

Wang, Sheng-De; Kuo, Te-Son; Hsu, Chen-Fa

IEEE Trans. Autom. Control 31, 654-656 (1986).

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

Keywords:

upper and lower bounds on the trace of the solutions; algebraic Riccati equation; Lyapunov equation; suboptimal feedback law