Homogeneity approach to high-order sliding mode design

By Arie Levant. at - Automatisierungstechnik, 2005

989 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/106df06cae8b10e97e9cd7a604bc27e8adf17f79

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In Control and Systems Engineering

Citations in the corpus

Continuous Integral Terminal Third-Order Sliding Mode Motion Control for Piezoelectric Nanopositioning System (2017, neutral): “finite time [37].”
Strict Lyapunov Functions for the Super-Twisting Algorithm (2012, background): “The states of the plant follow the typical limit cycle behavior, slightly perturbed by the presence of the perturbations and .”
Chattering Analysis (2007, background): “It is proved [23] that the accuracy is established in finite time with some positive constants independent of .”
A novel adaptive-gain supertwisting sliding mode controller: Methodology and application (2012, neutral): “(b) Using the higher order sliding mode control techniques (Djemaï, Barbot, & Busawon, 2008; Laghrouche, Plestan, & Glumineau, 2007; Laghrouche, Smaoui, Plestan, & Brun, 2006; Levant, 2003, 2005; Plestan, Glumineau, & Laghrouche, 2008; Shtessel, Shkolnikov, & Levant, 2007).”
Principles of 2-sliding mode design (2007, methodology): “At the same time design of new r-sliding controllers is rather difficult with r > 2 due to the complicated geometry of Rr (Floquet et al., 2003; Levant, 2003, 2005b).”
Smooth second-order sliding modes: Missile guidance application (2007, methodology): “The rest of the proof follows from Theorem 2 (Levant, 2005b).”
Finite-time and fixed-time stabilization: Implicit Lyapunov function approach (2015, background): “The theoretical background of HOSM control systems is very well developed (Levant, 2005a,b, 2007).”
Higher order sliding modes (2008, background): “Recently, generalized algorithms for designing universal arbitrary-order HOSM controllers have been developed based on the homogeneous [16] and quasi-homogeneous [17] properties of HOSM dynamics.”
A fixed-time output feedback control scheme for double integrator systems (2017, background): “Definition 6 [7] The origin of system (1) is said to be globally finite-time stable if it is Lyapunov stable and for any R > 0 exists T > 0, such that any trajectory starting within the ball ||x|| ≤ R stabilizes at the origin in the time T .”
Prescribed-Time Control and Its Latest Developments (2022, background): “The homogeneous approach, terminal sliding mode, higher-order sliding modes, and adding a power integrator are suggested sequentially in an attempt to achieve FT stability for high-order nonlinear systems [77], [78], [79], [80], [81], [82].”
A Lyapunov approach to second-order sliding mode controllers and observers (2008, methodology): “Instead, it is usual to use majorant curves or homogeneity based methods to study convergence [7], [8], [11], [15].”
Sliding mode control design using canonical homogeneous norm (2019, methodology): “The most popular dilations in R (see [13], [15], [12], [11], [14], [17] ) • uniform (or standard) dilation (L.”
Sliding-Mode-Based Differentiation and Its Application (2017, background): “Thus, according to Levant (2003, 2005), for sampling time periods not exceeding τ > 0 and the maximal possible sampling error ε ≥ 0 the differentiation accuracy |zi(t)− f (i)0 (t)| ≤ νiLρk+1−i, i = 0, 1, ..., k, ρ = max[(ε/L)1/(k+1), τ ] (8) is ensured, where the constant numbers νi ≥ 1 only depend…”