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Block Lyapunov sum with applications to integral controllability and maximal stability of singularly perturbed systems. (English) Zbl 0817.93009

Summary: A new block-structured Lyapunov sum for partitioned matrices is defined and basic properties are established. It has similar properties to a Lyapunov matrix, but preserves the block structure, and has similar properties to the block Kronecker sum, but with about half the dimension. It is used to solve a maximal stability problem of integral controllability, and is also used to solve for the maximal stability range of singularly perturbed systems. In both cases closed formulae are obtained with lower dimensions than existing formulae.

MSC:

93B11 System structure simplification
34D15 Singular perturbations of ordinary differential equations
93D15 Stabilization of systems by feedback
15A99 Basic linear algebra
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