Finite‐ and fixed‐settling time of real‐time differentiators utilising a higher‐order sliding mode (HOSM) observer based on both non‐recursive and recursive algorithm formulations are studied using constant observer gains. Fixed convergence time estimation is achieved independent of initial conditions of the differentiation errors. The corresponding convergence/settling times are estimated. The HOSM differentiators are compared with the ideal differentiation formulation and MATLAB's differentiator. The analysis incorporates input noise to demonstrate via simulations the improved performance for real‐time noisy input signals.

Finite- and fixed-settling time differentiators utilizing a nonrecursive higher order sliding mode (HOSM) observer are studied. Fixed convergence time estimation is achieved independent of initial conditions of the differentiation errors. The corresponding convergence/settling times are estimated. The finite- and fixed-time HOSM differentiators' performance is compared against the Levant recursive one via a hypersonic missile control simulation case study during the missile's terminal phase of flight. A continuous adaptive HOSM control is utilized. The double-layer adaptive algorithm is based on an equivalent control concept and does not allow overestimation of the control gains that mitigates control chattering. The robustness and high-accuracy output tracking in the presence of matched and unmatched external disturbances and missile model uncertainties is demonstrated for both the differentiators and the controller.

The contribution of this study is threefold. First, a vector (multivariable) super‐twisting algorithm is designed to provide a direct extension of the conventional scalar super‐twisting control, without any additional terms. An upper estimate of its convergence (settling) time is calculated. Second, a fixed‐time convergent continuous vector super‐twisting‐like algorithm is presented and its fixed convergence time is estimated. Third, an estimate of the finite convergence time of the scalar super‐twisting algorithm is obtained as a particular case of the vector super‐twisting one, which occurs to be less conservative than the one derived specially for the scalar case. The proposed theoretical concepts are illustrated in a number of scalar and multivariable examples.

This paper studies the observer-based adaptive fuzzy tracking control problem for a general class of multi-input-single-output nonstrict-feedback systems subject to unmeasured states and actuator failures. For actuator failures, both cases of lock-in-place and loss of effectiveness are synchronously considered. To handle the unknown nonlinear functions, fuzzy logic systems are employed. By constructing a fuzzy observer and a serial-parallel estimation model, the unmeasured states are estimated and the accuracy of approximating the unknown functions is improved. Moreover, taking into account the prediction error between the fuzzy observer and the serial-parallel estimation model, a novel composite fuzzy output-feedback control scheme is developed. Unlike some existing control schemes for systems with actuator failures, the developed control scheme allows one to avoid the problem of “explosion of complexity” and improve the approximation performance. It is proved that all signals in the system are bounded and the tracking error converges to a small neighborhood of the origin by choosing appropriate parameters. Finally, the effectiveness of the proposed method is confirmed via simulation examples with actuator failures.

The stability and stabilization problems for a class of switched discrete-time nonlinear systems are studied in this paper. Each nonlinear subsystem of the presented switched system is modeled as a piecewise affine (PWA) one by splitting the state space into polyhedron regions. With the aid of a simple searching strategy for active state transition pairs at a switching instant, i.e., the so-called $\mathbb {S}$ -arbitrary switching approach, the stability criteria are derived via the relaxed piecewise quadratic Lyapunov function technique. Then, using the descriptor system approach, a family of PWA stabilizing controllers are designed to guarantee exponential stability of the resulting closed-loop control system, and the corresponding PWA controller gains could be calculated using numerical software. The validity and potential of the developed techniques are verified through a numerical example.