# Backstepping controller synthesis and characterizations of incremental stability

@article{Zamani2013BacksteppingCS, title={Backstepping controller synthesis and characterizations of incremental stability}, author={Majid Zamani and Nathan van de Wouw and Rupak Majumdar}, journal={Syst. Control. Lett.}, year={2013}, volume={62}, pages={949-962} }

Incremental stability is a property of dynamical and control systems, requiring the uniform asymptotic stability of every trajectory, rather than that of an equilibrium point or a particular time-varying trajectory. Similarly to stability, Lyapunov functions and contraction metrics play important roles in the study of incremental stability. In this paper, we provide characterizations and descriptions of incremental stability in terms of existence of coordinate-invariant notions of incremental…

## 32 Citations

Controller synthesis for incremental stability: Application to symbolic controller synthesis

- Computer Science, Mathematics2013 European Control Conference (ECC)
- 2013

A recursive way of constructing incremental Lyapunov functions which have been identified as a key tool enabling the construction of finite abstractions of nonlinear control systems is proposed.

Backstepping design for incremental stability of stochastic Hamiltonian systems

- Mathematics, Computer Science2016 IEEE 55th Conference on Decision and Control (CDC)
- 2016

This work provides a backstepping controller design scheme providing controllers along with corresponding incremental Lyapunov functions rendering a class of stochastic control systems, namely stoChastic Hamiltonian systems, incrementally stable.

Backstepping Design for Incremental Stability of Stochastic Hamiltonian Systems with Jumps

- Mathematics, Computer ScienceIEEE Trans. Autom. Control.
- 2018

A backstepping controller design scheme is provided providing controllers along with corresponding incremental Lyapunov functions rendering a class of stochastic control systems, namely, stochastically Hamiltonian systems with jumps, incrementally stable.

Distance function design and Lyapunov techniques for the stability of hybrid trajectories

- Computer Science, MathematicsAutom.
- 2016

A generic distance function is designed that can be used to circumvent the so-called "peaking phenomenon" when using the Euclidean distance to compare two hybrid trajectories, and a tracking controller is presented that asymptotically stabilises a given hybrid reference trajectory.

Constructing distance functions and piecewise quadratic Lyapunov functions for stability of hybrid trajectories

- Computer Science, Mathematics2015 54th IEEE Conference on Decision and Control (CDC)
- 2015

A novel and systematic way of designing appropriate distance functions is proposed that overcomes this hurdle and enables the derivation of sufficient Lyapunov-type conditions, using minimal or maximal average dwell-time arguments, for the stability of a hybrid trajectory.

Incremental passivity and stabilization for switched nonlinear systems

- Computer ScienceTrans. Inst. Meas. Control
- 2020

A recursive feedback incremental passification design technique is adopted to achieve the incremental stability for a switched nonlinear system with any same relative degree by designing a set of feedback controllers and a state-dependent switching law, constructively.

Approximately symbolic models for a class of continuous-time nonlinear systems

- Computer Science, Engineering2019 IEEE 58th Conference on Decision and Control (CDC)
- 2019

A novel stability notion called controlled globally asymptotic/practical stability with respect to a set is proposed and it is shown that every system, under the condition that there exists an admissible control interface such that the augmented system can be made controlled globally practically stable withrespect to the given set, is approximately simulated by its discrete abstraction.

Checkable Conditions for Contraction After Small Transients in Time and Amplitude

- Mathematics
- 2017

Contraction theory is a powerful tool for proving asymptotic properties of nonlinear dynamical systems including convergence to an attractor and entrainment to a periodic excitation. We consider…

Periodic optimal control of nonlinear constrained systems using economic model predictive control

- Engineering, Computer ScienceArXiv
- 2020

The proposed economic MPC scheme uses an online optimized artificial periodic orbit to ensure recursive feasibility and constraint satisfaction despite unpredictable changes in the economic performance index.

Contraction after small transients

- Mathematics, Computer ScienceAutom.
- 2016

This work considers three generalizations of contraction with respect to a norm that allow contraction to take place after small transients in time and/or amplitude.

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