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Note the condition of stability for a fractional-order system (1.3a - 1.3d 1.3a - 1.3d
The Lyapunov function is important for stability theory and control theory, and its existence is a necessary and sufficient condition of stability for many differential equation systems.
The conditions for oscillation lead to the problem of the boundary regions of Mathieu functions where Melaclan [11] gives the condition of stability as | Δ ( 0 ) sin 2 ( π a 2 ) | 1 2 ≤ 1 (50).
It is well-known that for a nonautonomous system with the complex eigenvalues λ j ( t ), j = 1, …, n, the classical Routh-Hurvitz condition of stability Re [ λ j ] ≤ 0, j = 1, …, n, fails.
The sufficient condition of stability of the proposed schemes has been derived and expressed as a linear matrix inequality (LMI) optimization problem and the design parameters of the observers are determined by using LMI techniques.
With the proof that the stochastic communication logic is essentially a Markov chain, the NCS is modeled as a jump system and the necessary and sufficient condition of stability for the state feedback system is presented as well.
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A corresponding Lyapunov function is constructed to achieve sufficient conditions of stability and stabilization.
When α="1 and E=I, the three results reduce to the conditions of stability and robust stabilization of normal integer order systems.
"There is a huge amount of work to do in rebuilding Mali and creating the conditions of stability that will bring the country back to democracy".
But on the ground, one can begin to see the green shoots of progress and, in Garmsir, the conditions of stability and Britain's eventual withdrawal.
In particular, there is a focus on the conditions of stability, integration, and effectiveness of the system.
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