Further Stability and Stabilization Condition for Sampled-Data Control Systems via Looped-Functional Method
S. Lakshmanan, Young Hoon Joo
Abstract
This brief contributes the further results on stability and stabilization conditions for sampled-data-based control systems (SDCSs), which include linear SDCSs and nonlinear SDCSs via looped-Lyapunov functional approach. The improved Lyapunov functional involves the states information such as x(t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> ) and x(t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k+1</sub> ) with few slack variables and a tuning parameter. The sufficient conditions are derived for both linear SDCSs and nonlinear SDCSs, whereas Takagi-Sugeno (T-S) approach is employed to express the nonlinear SDCS into T-S fuzzy-based model through fuzzy IF-THEN membership rules. With the derived conditions, the stability region of the proposed SDCSs can be enhanced and their asymptotic stability will be ensured. Finally, the numerical analysis is performed with the existing models and their corresponding performances are provided to validate the less conservatism and superiority of the derived results over the existing ones.