Abstract
Narendra and Balakrishnan proposed a way to construct a common quadratic Lyapunov function (CQLF) [1], whena set of stable matrices are commutative. The purpose of this paper is to generalize the method to non-commutative and non-solvable case. A modified constructing algorithm is proposed and certain conditions are provided to assure the resulting matrix being a CQLF. Next, the problem discussed is when a stable matrix can be added to a set of matrices with CQLF to construct a new CQLF for the enlarged set.
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