Improved stability and stabilization criteria of sampled-data control systems based on an enhanced looped-functional

Abstract

This paper proposes improved stability and stabilization criteria that can increase the upper bound of sampling interval for the sampled-data systems while decreasing the computational complexity. To realize such improvement, an enhanced looped-functional is devised so that it can include 1) two time integrals of the weighted state derivative and 2) a single-integral quadratic terms with an augmented vector stacked with the state and its derivative. In addition, to aid the efficient use of the looped-functional, two zero equalities are newly established in the main derivation, which plays a key role in reinforcing the relationship between the time integrals of the weighted state derivative and other considered states. Furthermore, an improved free-matrix-based integral inequality is provided to obtain a tight upper bound on the single-integral quadratic terms in the stability analysis and control synthesis process. Finally, the validity of proposed method is verified through three numerical examples.