Robust stabilization of nonlinear systems: The LMI approach

By Dragoslav D. Siljak, Dusan M. Stipanovic. 2000

284 citations recorded by the source corpus.

This paper presents a new approach to robust quadratic stabilization of nonlinear systems within the framework of Linear Matrix Inequalities (LMI). The systems are composed of a linear constant part perturbed by an additive nonlinearity which depends discontinuously on both time and state. The only information about the nonlinearity is that it satisfies a quadratic constraint. Our major objective is to show how linear constant feedback laws can be formulated to stabilize this type of systems and, at the same time, maximize the bounds on the nonlinearity which the system can tolerate without going unstable.

Subfields: Control and Systems Engineering, Electronic, Optical and Magnetic Materials

View Paper: https://www.semanticscholar.org/paper/c2371e035f4a4e26e6291087aae38374685562db

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In Control and Systems Engineering

In Electronic, Optical and Magnetic Materials

Citations in the corpus

Decentralized overlapping control of a formation of unmanned aerial vehicles (2002, methodology): “In other words, the idea is to split vector zi into two subvectors, where the ;rst subvector zI i includes position coordinates and the second subvector zII i includes speed coordinates of the ith vehicle. This type of decomposition is chosen due to diRerent treatment of the state variables, that is”
State feedback controller design of networked control systems with interval time‐varying delay and nonlinearity (2008, background): “[30] System (2) is robustly asymptotically stable with degree α if the equilibrium x = 0 is globally asymptotically stable for all h(t, x(t)) ∈ Hα.”
Robust Decentralized Turbine/Governor Control Using Linear Matrix Inequalities (2002, methodology): “To limit the gain and, at the same time, guarantee a desired value for each subsystem, we apply the following modification of the optimization problem [27].”
Event‐triggered H∞ control for a class of nonlinear networked control systems using novel integral inequalities (2017, background): “Denote H WD ® ' W RnC1 ! R ˇ̌ ' ' 6 'DD' in the domains of continuity ̄ (74) The robust stabilization problem of the system (72) was addressed in detail in [42].”