Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  proposes a new approach to stabilize switched linear systems. In this method, the projections are employed to establish the stabilization of a switched systems class. Hence,  suppose that the subsystems given by a switched linear system can be projected to the same subspace. Under these conditions,  prove that this switched linear system is stabilizable if and only if a low-order switched linear system is also stabilizable. In order to complete this study,  present a counter example that proves that it is not always possible to use the projections. Moreover, the main result in the paper is applied to solve the stabilization of a third-order switched systems class and the static feedback stabilization of a switched linear systems class. Finally, a numerical example is included in order to illustrate the new method obtained to stabilize a third-order switched systems class.
['Carmen Pérez', 'Francisco Carpintero Benítez', 'J.B. García-Gutiérrez']
I am writing a research paper on a idea Stabilization of switched linear systems by using projections
[{"from": "human", "value": "I am writing a research paper on a idea Stabilization of switched linear systems by using projections"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  proposes a new approach to stabilize switched linear systems. In this method, the projections are employed to establish the stabilization of a switched systems class. Hence,  suppose that the subsystems given by a switched linear system can be projected to the same subspace. Under these conditions,  prove that this switched linear system is stabilizable if and only if a low-order switched linear system is also stabilizable. In order to complete this study,  present a counter example that proves that it is not always possible to use the projections. Moreover, the main result in the paper is applied to solve the stabilization of a third-order switched systems class and the static feedback stabilization of a switched linear systems class. Finally, a numerical example is included in order to illustrate the new method obtained to stabilize a third-order switched systems class."}]