Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies switching stabilization problems for continuous-time switched linear systems (SLSs).  consider the most general switching stabilizability defined as the existence of a measurable switching signal under which the resulting time-varying system is asymptotically stable. In addition,  consider feedback stabilizability in Filippov sense defined as the existence of a switching law under which the closed-loop Filippov solution is asymptotically stable.  develop sufficient and necessary conditions for switching stabilizability as ll as feedback stabilizability in Filippov sense. It is proved that for continuous-time SLSs, both switching stabilizability and feedback stabilizability in Filippov sense are equivalent to the existence of a piecewise quadratic control-Lyapunov function (CLF). Furthermore, such a CLF can be obtained by taking the pointwise minimum of a finite number of quadratic functions.
['Yueyun Lu', 'Wei Zhang']
I am writing a research paper on a idea Converse control-Lyapunov function theorems for continuous-time switched linear systems
[{"from": "human", "value": "I am writing a research paper on a idea Converse control-Lyapunov function theorems for continuous-time switched linear systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies switching stabilization problems for continuous-time switched linear systems (SLSs).  consider the most general switching stabilizability defined as the existence of a measurable switching signal under which the resulting time-varying system is asymptotically stable. In addition,  consider feedback stabilizability in Filippov sense defined as the existence of a switching law under which the closed-loop Filippov solution is asymptotically stable.  develop sufficient and necessary conditions for switching stabilizability as ll as feedback stabilizability in Filippov sense. It is proved that for continuous-time SLSs, both switching stabilizability and feedback stabilizability in Filippov sense are equivalent to the existence of a piecewise quadratic control-Lyapunov function (CLF). Furthermore, such a CLF can be obtained by taking the pointwise minimum of a finite number of quadratic functions."}]