A continuous feedback approach to global strong stabilization of nonlinear systems

By Chunjiang Qian, Wei Lin. IEEE Transactions on Automatic Control, 2001

1,338 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/3679953e1f2209ab728b626420999811b2f7bfcf

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In Control and Systems Engineering

1. Shihua Li
2. Peng Shi
3. Chunjiang Qian
4. Yanjun Shen
5. Shuzhi Sam Ge
6. Shaocheng Tong
7. S. Khoo
8. Jason Polendo

Citations in the corpus

• Semi-global finite-time observers for nonlinear systems (2008, methodology): “The major technique used is homogeneity (Qian & Lin, 2001).”
• Global control of nonlinear systems with uncertain output function using homogeneous domination approach (2012, background): “The proofs of the lemmas can be found in many existing papers, for example [31].”
• State‐feedback stabilization for a class of more general high order stochastic nonholonomic systems (2011, background): “In [17], for a class of systems whose nonlinearities fi (·) rely on (x1, .”
• A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems (2005, positive): “This idea has been very successful in the state-feedback stabilization of a class of nonlinear systems without controllable/observerable linearization [5], [6], [11], [1], [19].”
• Adaptive Robust Finite-Time Trajectory Tracking Control of Fully Actuated Marine Surface Vehicles (2016, methodology): “Lemma 3 [25]: For any x ∈ R, y ∈ R, c > 0, d > 0, |x |c|y|d ≤ (c/(c + d))|x |c+d + (d/(c + d))|y|c+d .”
• A general framework for tackling the output regulation problem (2004, methodology): “Noting the function is satisfying , and with compact set, and using a well known inequality as can be found in [32] and [33], we have”
• Sliding Mode Direct Yaw-Moment Control Design for In-Wheel Electric Vehicles (2017, methodology): “Lemma 2 ([27]): Let v and w be positive constants.”
• Global stabilization of a class of uncertain upper‐triangular systems under sampled‐data control (2013, background): “13) The proof of this inequality is mainly based on the feedback domination design [16] because of the presence of the uncertain coefficients in (2.”
• Finite‐time output feedback stabilization of nonlinear high‐order feedforward systems (2016, methodology): “Lemma 1 ([31]) For x, y 2 R, and p > 1 are a constant, then jx C yj 6 2 (1)jx C yj; (3)”
• Robust control of uncertain systems with polynomial nonlinearity by output feedback (2009, background): “Moreover, there exists a virtual controller of the form (as proceeded in Section 3 or [7]) x∗p1···pk k+1 =− k+1( k+ gk+1 pk gk k ) (72)”
• Global stabilization of a class of upper‐triangular systems with unbounded or uncontrollable linearizations (2011, background): “The next two lemmas, given without proofs which can be found in [19], play very important roles in constructing the controller.”
• A generalized homogeneous domination approach for global stabilization of inherently nonlinear systems via output feedback (2007, methodology): “feedback problem was resolved in [16] for the stabilization of systems such as (1) with pi51 being odd integers and fið Þ bounded by a lower-triangular C(1) function vanishing at the origin.”
• Smooth output feedback stabilization for a class of nonlinear systems with time‐varying powers (2017, methodology): “To solve the aforementioned difficulties and fill the gap of lacking methods in the literature for the unsolved global stabilization problem of system (1), in this paper, we first design a smooth state feedback globally stabilizing controller by revamping the adding a power integrator technique [11,”
• Fixed-Time Attitude Control for Rigid Spacecraft With Actuator Saturation and Faults (2016, neutral): “Lemma 2 [17]: For any xi ∈ R, (∑i=1 |xi |)v ≤ ∑n i=1 |xi |v, where v ∈ R+ and v ∈ (0, 1].”
• Finite-Time Attitude Tracking Control of Spacecraft With Application to Attitude Synchronization (2011, methodology): “Lemma 2: [18]: If , where are positive odd integers, then .”
• Technical Notes and Correspondence Uniformly Observable and Globally Lipschitzian Nonlinear Systems Admit Global Finite-Time Observers (2009, methodology): “By extending the adding-a-power-integrator technique [ 7 ], [8] and a special continuous observer design, a dynamic output feedback controllerwas explicitlydeveloped to rendera class of continuous but nonsmooth nonlinear systems globally finite-time stable [9].”