Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Necessary and sufficient Liapunov-like conditions for both absolute stability and the Aizerman conjecture are established in the framework of stationary, continuous-time Lurie-Postnikov systems with multiple nonlinearities, thus providing theoretical solutions for these problems in the Liapunov sense. The solutions are based on the use of functional families instead of a single Liapunov function. Directly applicable results of the paper are new algebraic criteria for absolute stability. One of them is proved by using a new form of a tentative system Liapunov function. Also an estimate of the asymptotic stability domain is determined for all admissible nonlinearities. The results do not impose any requirement on the linear part of the system (such as its stability or controllability or observability). Three illustrative examples are worked out.
['Ljubomir T. Gruji']
I am writing a research paper on a idea Paper: On absolute stability and the aizerman conjecture
[{"from": "human", "value": "I am writing a research paper on a idea Paper: On absolute stability and the aizerman conjecture"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Necessary and sufficient Liapunov-like conditions for both absolute stability and the Aizerman conjecture are established in the framework of stationary, continuous-time Lurie-Postnikov systems with multiple nonlinearities, thus providing theoretical solutions for these problems in the Liapunov sense. The solutions are based on the use of functional families instead of a single Liapunov function. Directly applicable results of the paper are new algebraic criteria for absolute stability. One of them is proved by using a new form of a tentative system Liapunov function. Also an estimate of the asymptotic stability domain is determined for all admissible nonlinearities. The results do not impose any requirement on the linear part of the system (such as its stability or controllability or observability). Three illustrative examples are worked out."}]