Applying output feedback integral sliding mode controller to uncertain time-delay systems with mismatched disturbances

Abstract

For time-delay systems with mismatched disturbances and uncertainties, this paper develops an integral sliding mode control algorithm using output information only to stabilize the systems. An integral sliding surface is comprised of output signals and an auxiliary full-order compensator. The proposed output feedback sliding mode controller can satisfy the reaching and sliding condition and maintain the system on the sliding surface from the initial moment. When two specific algebraic Riccati inequalities have solutions, our method can guarantee the stability of the closed-loop system and satisfy the property of robust disturbance attenuation. Moreover, the design parameters of controller and compensator can be simultaneously determined by solutions to the algebraic Riccati inequalities. Finally, two numerical examples illustrate the applicability of the proposed scheme.

Finite‐Time Output Feedback Controller Based on Observer for the Time‐Varying Delayed Systems: A Moore‐Penrose Inverse Approach

“…Assumptions 1, 2, and 3 are standard assumptions for time-delay systems which can be found in most existing literatures. For Assumption 4, in recent studies [4][5][6][7], it is required in this technical note that the exogenous disturbances must be bounded by a known function of the outputs. In practical cases, these conditions are often difficult to meet.…”

“…It commonly leads to an instability and/or reduces the system performance in the closed-loop system [3]; hence, the stability of the time-delay uncertain system has been attracting the interest of a large number of quality papers published in the most recently internationally renowned journals [4][5][6][7][8] and the related references therein. Thanks are due to some distinguished features of the VSC such as finite-time convergence, fast dynamic response, good robustness, exogenous perturbations rejection ability, and its insensitivity to parameter variations.…”

“…In many practical systems, the state variables are not measured directly or the number of measuring devices is limited. Hence, the works of OFC based on FOOs/ROOs were investigated by many authors [4][5][6][7][8]28]. In [28], the OFC was represented for Itô stochastic time-delay systems by utilizing the FOO tool and measured output.…”

“…But the obtained results could not ensure invariance to the matched uncertainties in sliding mode. The work [6] established OFC which was assumed to satisfy the norm of unmeasured states with known nonnegative constant value. This constant value is not easily achieved in practice.…”

“…In [5], the OFC was proposed, which assumed that the norm of states and norm of observer error have to be bounded output signal, for a class of uncertain neural systems with unmeasured states. It should be pointed out that the recent works [4][5][6][7] have some serious limitations, where it is required that the exogenous disturbances must be bounded by a known function of the outputs. Moreover, all published works have represented the OFC based on FOO, which increases the computation of burden due to the associated closed-loop systems.…”