Abstract.
We consider the computation of Hermitian nonnegative definite solutions of algebraic Riccati equations. These solutions are the limit, P=limi →∞ P i, of a sequence of matrices obtained by solving a sequence of Lyapunov equations. The procedure parallels the well-known Kleinman technique but the stabilizability condition on the underlying linear time-invariant system is removed. The convergence of the constructed sequence {P i }i≥1 is guaranteed by the minimality of P i in the set of Hermitian nonnegative definite solutions of the Lyapunov equation in the ith iteration step.
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Date received: October 21, 1999. Date revised: February 14, 2002.
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ID="*"This work was supported by the Acciones Integradas programme of Deutscher Akademischer Austauschdienst (Germany) and Dirección General de Infraestructura y Relaciones Internacionales (Spain).
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Benner, P., Hernández, V. & Pastor, A. The Kleinman Iteration for Nonstabilizable Systems. Math. Control Signals Systems 16, 76–93 (2003). https://doi.org/10.1007/s00498-003-0130-z
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DOI: https://doi.org/10.1007/s00498-003-0130-z