Synthesis of Stabilization Control on Outputs for a Class of Continuous and Pulse-Modulated Undefined Systems
Mathematics
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Abstract
Consider system where x1, …, and xn is the state of the system, u1, …, and ul are controls, n/l is not an integer, and l ≥ 2. It is supposed that only outputs x1, …, and xl are measurable, (l > n) and ϕi(·) are non-anticipating arbitrary functionals, and 0 < ρ–≤ ρi (t, x1, …, and xl) ≤ ρ+. Using the backstepping method, we construct the square Lyapunov function and stabilize the control for the global exponential stability of the closed loop system. The stabilization by means of synchronous modulators with a sufficiently high impulsion frequency is considered as well.
$$\left\{ {\begin{array}{*{20}{c}}
{{{\dot x}_1} = {\varphi _1}(.) + {\rho _1}{x_{l + 1}},} \\
{{{\dot x}_m} = {\varphi _m}(.) + {\rho _m}{x_n},} \\
{{{\dot x}_{m + 1}} = {\varphi _{m + 1}}(.) + {\mu _1},} \\
{{{\dot x}_n} = {\varphi _n}(.) + {\mu _1},}
\end{array}} \right.$$
Keywords
uncertain systems output stabilization global exponential stabilityPreview
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