Homogeneous Approximation, Recursive Observer Design, and Output Feedback

By Vincent Andrieu, Laurent Praly, Alessandro Astolfi. SIAM Journal of Control and Optimization, 2008

866 citations recorded by the source corpus.

We introduce two new tools that can be useful in nonlinear observer and output feedback design. The first one is a simple extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability and robustness for a homogeneous in the bi-limit vector field. The second tool is a new recursive observer design procedure for a chain of integrator. Combining these two tools, we propose a new global asymptotic stabilization result by output feedback for feedback and feedforward systems.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/b98abd82fbc0b6f751f58de8d7778d47ecf20c37

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In Control and Systems Engineering

Citations in the corpus

An Overview of Recent Advances in Fixed-Time Cooperative Control of Multiagent Systems (2018, methodology): “A similar result is derived in [36] based on a bilimit homogeneity technique [37] instead of the Lyapunov method.”
A class of predefined-time stable dynamical systems (2018, methodology): “Roxin (1966), Weiss and Infante (1967), Michel and Porter (1972), Ryan (1991), Bhat and Bernstein (2000), Hong (2002), Orlov (2005), Moulay and Perruquetti (2006) for finite-time stability, Andrieu et al. (2008), Cruz-Zavala et al. (2010), Polyakov (2012) for fixed-time stability, and Smith (1957), ”
Uniform Robust Exact Differentiator (2010, background): “Our work has many differences with [1], e.”
A Lyapunov-Like Characterization of Predefined-Time Stability (2019, background): “Example 2: Consider system (see [6] and [8])”
On optimal predefined‐time stabilization (2017, background): “[20] for homogeneous systems, and it was proposed in [21–23] for systems with sliding modes.”
Fixed-Time Consensus Tracking for Multiagent Systems With High-Order Integrator Dynamics (2018, background): “The proof of [28, Lemma 2] is based on the bilimit homogeneity [30].”
A fixed-time output feedback control scheme for double integrator systems (2017, background): “Definition 3 [12] A function g(x) : R → R is said to be homogeneous in the p-limit (p=0 or ∞) with triple (rp, kp, gp), where rp = [rp,1, .”
Sliding mode control design using canonical homogeneous norm (2019, background): “The most popular dilations in R (see [13], [15], [12], [11], [14], [17] ) • uniform (or standard) dilation (L.”