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The convergence stability of the observer is proved based on a Lyapunov analysis assisted by physical insights into the engine/combustion systems.
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In addition, the properties will be proved based on an implicit representation of the equations, in comparison with previous approaches [18, 19], where an explicit description of the model is obtained prior to analysis.
It has been proved based on Besov space norm theory.
Existence and equivalence of the solution are analyzed and proved based on Brouwer fixed point theorem.
Then, the asymptotic stability of the system is proved based on the Lyapunov method.
The convergence of the switching control is proved based on state sample trajectories.
The significance of velocity uniformity is proved based on the analysis and experiment.
The stability of the proposed scheme is proved based on the Lyapunov analysis method.
Their robustness is proved based on the proposed Lyapunov equation approach.
The stability of the overall closed-loop system is proved based on Lyapunov theory.
The closed system's stability is proved based on the fractional order stability theory.
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