Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  derive sufficient conditions on drift matrices under which block-diagonal solutions to Lyapunov inequalities exist. The motivation for the problem comes from a recently proposed basis pursuit algorithm. In particular, this algorithm can provide approximate solutions to optimisation programmes with constraints involving Lyapunov inequalities using linear or second order cone programming. This algorithm requires an initial feasible point, which  aim to provide in this paper. Our existence conditions are based on the so-called ℋ matrices.  also establish a link beten ℋ matrices and an application of a small gain theorem to the drift matrix.  finally show how to construct these solutions in some cases without solving the full Lyapunov inequality.
['Aviar Sootla', 'James Anderson']
I am writing a research paper on a idea On existence of solutions to structured lyapunov inequalities
[{"from": "human", "value": "I am writing a research paper on a idea On existence of solutions to structured lyapunov inequalities"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  derive sufficient conditions on drift matrices under which block-diagonal solutions to Lyapunov inequalities exist. The motivation for the problem comes from a recently proposed basis pursuit algorithm. In particular, this algorithm can provide approximate solutions to optimisation programmes with constraints involving Lyapunov inequalities using linear or second order cone programming. This algorithm requires an initial feasible point, which  aim to provide in this paper. Our existence conditions are based on the so-called \u210b matrices.  also establish a link beten \u210b matrices and an application of a small gain theorem to the drift matrix.  finally show how to construct these solutions in some cases without solving the full Lyapunov inequality."}]