Nonlinear norm-observability notions and stability of switched systems

By João Pedra Hespanha, Daniel Liberzon, David Angeli, Eduardo Sontag. IEEE Transactions on Automatic Control, 2005

313 citations recorded by the source corpus.

This work proposes several definitions of "norm-observability" for nonlinear systems and explores relationships among them. These observability properties involve the existence of a bound on the norm of the state in terms of the norms of the output and the input on some time interval. A Lyapunov-like sufficient condition for norm-observability is also obtained. As an application, we prove several variants of LaSalle's stability theorem for switched nonlinear systems. These results are demonstrated to be useful for control design in the presence of switching as well as for developing stability results of Popov type for switched feedback systems.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/be591682dba99dab28d122a145a18615d2179643

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In Control and Systems Engineering

Citations in the corpus

Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results (2009, background): “tion, which is conservative in the sense that there are switched systems that can be asymptotically or even exponentially stabilized without using a common quadratic Lyapunov function [36].”
Hybrid Control for Connectivity Preserving Flocking (2009, background): “Our argument is along the lines of [12]: suppose that this is not true.”
Dissipativity Theory for Switched Systems (2005, background): “4: This asymptotic zero-state detectability is a weaker version of small-time norm observability [14].”
On the observability and identifiability of nonlinear structural and mechanical systems (2015, background): “The fact that piecewise systems have different observability properties than each of their individual analytic branches has been stressed for piecewise linear systems ([38] and [39]) and switched nonlinear systems [40].”
Flocking in Fixed and Switching Networks (2007, background): “Here, the stability analysis can be based on recent results for switched nonlinear systems [29].”
Effects of Delay in Multi-Agent Consensus and Oscillator Synchronization (2010, background): “This behavior is the main difference to the proof in [32] where has to be uniformly continuous in all intervals .”
Flocking of multi‐agent dynamical systems with intermittent nonlinear velocity measurements (2012, background): “M q.t/ , p.t// is a common weak Lyapunov function of the multi-agent system (1) [42].”
Adaptive Fuzzy Control for Nontriangular Structural Stochastic Switched Nonlinear Systems With Full State Constraints (2019, background): “INTRODUCTION SWITCHED systems, as a typical class of hybrid systems, have received considerable research attention [1]–[4].”
Invariance Principles for Hybrid Systems With Connections to Detectability and Asymptotic Stability (2007, background): “The follow-up work, [27], extends some of the results of [26] to a family of nonlinear switched systems under a larger set o f”