Robust stability analysis and implementation of Persidskii systems

IEEE Trans. Automat. Contr.

et al. 2022

For a class of generalized Persidskii systems, whose dynamics are described by superposition of a linear part with multiple sector nonlinearities and exogenous perturbations, the conditions of practical stability, instability and oscillatory behavior in the sense of Yakubovich are established. For this purpose the conditions of local instability at the origin and global boundedness of solutions (practical input-to-state stability) are developed in the form of linear matrix inequalities. The proposed theory is applied to investigate robustness to unmodeled dynamics of nonlinear feedback controls in linear systems, and to determine the presence of oscillations in the models of neurons.

Section: Introductionmentioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Conditions of Self-Oscillations in Generalized Persidskii Systems

Wang

Mendoza‐Avila

IEEE Trans. Automat. Contr.

et al. 2022

“…A sufficient condition for a system to be ISS is that there exists a positive definite and radially unbounded ISS Lyapunov function V : R n → R + for whichV ≤ −α( x ) + σ ( d ) holds for all x and d with some α ∈ K ∞ and σ ∈ K [20]. We use this for the following Lyapunovfunction borrowed from [21], which we need to prove our main result afterwards. Lemma 1.…”

Section: Unobservable Subspacementioning

confidence: 99%

A simple finite-time distributed observer design for linear time-invariant systems

Silm

Systems & Control Letters

Michiels

et al. 2020

A design of a distributed observer is proposed for continuous-time systems with nonlinear observer nodes such that the estimation errors converge in a finite time to zero. By taking advantage of individual observability decompositions, the designs for the locally observable and the unobservable substate are made independent from each other. For the observable substate of each node, standard centralized finite-time observer techniques are applied. To estimate distributively the unobservable substate, the observer nodes employ consensus coupling in a linear term and an additional term embedded in a fractional power. The approach is derived using homogeneity arguments and it leads to a simple design with an LMI that is guaranteed to be feasible under general conditions.

“…is a bounded input vector, whose norm is proportional to d, d. Following [25], consider a candidate Lyapunov function:…”

Section: Interval Predictor Designmentioning

confidence: 99%

Interval Prediction for Continuous-Time Systems with Parametric Uncertainties

Leurent

2019 IEEE 58th Conference on Decision and Control (CDC)

Raïssi

et al. 2019

The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all uncertainties take values in a given admissible set. Then an interval predictor is designed and its stability is guaranteed applying Lyapunov function with a novel structure. The conditions of stability are formulated in the form of linear matrix inequalities. Efficiency of the theoretical results is demonstrated in the application to safe motion planning for autonomous vehicles.