An Easy-to-Compute Criterion for Stability of Matrix Polytopes
Hideki Kokame, Hiroshi KIDA, Takehiro Mori · Transactions of the Society of Instrument and Control Engineers · 1990
In the case where stability of a linear system with uncertain parameters is concerned, realizable system matrices are often described as a polytope of matrices. However, stability condition of a matrix polytope has not been fully developed and moreover easy-to-compute stability criteria are few. Among them is such that if a positive-definite quadratic form be a common Lyapunov function for all vertex members of the polytope, then the matrix polytope is stable.In this paper, this criterion is extended to the case where a number of positive-definite quadratic forms are available, leading to a new easy-to-compute criterion which can assure stability for a wider class of problems. This stability criterion can be performed on a standard routine for linear programming. The class of multi-tuples of quadratic forms that satisfy the stability criterion is characterized in relation to other classes of the similar meaning. A systematic use of the proposed criterion for stability of perturbed systems is demonstrated by an example.