Input to State Stability: Basic Concepts and Results

By Eduardo Sontag. 2008

1,318 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/83496eb2edfb7a730c88a93258f86afaea061c40

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Citations in the corpus

String Stability and a Delay-Based Spacing Policy for Vehicle Platoons Subject to Disturbances (2017, background): “The notion of input/output-to-state stability in [34] (see also [33]) provides such a property.”
Input-to-State Stabilizing Control for Cyber-Physical Systems With Multiple Transmission Channels Under Denial of Service (2018, background): “Definition 1 (see [18]): System (1) is said to be input-to-state stable (ISS) if there exist a K L-function f1 and a K∞-function f2 such that, for each d(t) ∈ L∞(R≥0) and x(0) ∈ Rn ||x(t)|| ≤ f1(||x(0)||, t) + f2(||dt ||∞) (5)”
Characterizations of integral input-to-state stability for bilinear systems in infinite dimensions (2014, background): “We emphasize that the above definition does not yet exactly correspond to ISS of finite dimensional systems [40] since Definition 2.”
Formation Control and Collision Avoidance for Multi-agent Non-holonomic Systems: Theory and Experiments (2008, methodology): “It can be easily shown, using the ISS-Lyapunov function V 1 2 e 2 , that this system is input-to-state stable (ISS see Sontag (2006)) with respect to the input d and that the output is bounded for bounded values of the input Vd.”
Event-triggered control for discrete-time systems (2010, methodology): “The nominal system is assumed to be Input-to-State stable [19], with respect to measurement errors and then, tools from perturbation analysis of nonlinear systems are used in order to analyze the performance of the event-driven system.”
Input-to-State Stabilizing Control Under Denial-of-Service (2015, neutral): “[26]) Let Σ be the control system resulting from (1) under a control signal as in (6).”
Learning Stable Nonlinear Dynamical Systems With Gaussian Mixture Models (2011, background): “The stability of the inner loop requires the system to be input-to-state stable (ISS) [6], i.e., the output of the inner loop should remain bounded for a bounded input.”
A Dynamical System-based Approach to Modeling Stable Robot Control Policies via Imitation Learning (2012, background): “The stability of the inner loop requires the system to be Input-to-State Stable (ISS) (Sontag, 2008), i.”
Characterizations of input-to-state stability for hybrid systems (2009, background): “In particular, ISS for continuous-time systems, introduced in [16], is a basic concept for studying robust dynamical behaviors of nonlinear control systems affected by inputs, noise, or disturbances [17,10]; two key results related to ISS for continuous-time and discrete-time systems are that ISS is”
To Sample or not to Sample: Self-Triggered Control for Nonlinear Systems (2008, neutral): “We will not resort to the standard definition of input-to-state stability (ISS) (see [29] for details) in this paper but rather to the following characterization.”
A Small-Gain Approach to Robust Event-Triggered Control of Nonlinear Systems (2015, methodology): “Sontag, is a powerful tool to describe the stability property of nonlinear systems with external inputs [26].”
Strict Lyapunov functions for semilinear parabolic partial differential equations (2011, methodology): “the recent survey [28]) and, for a few years, begins to be used in the domain of the systems with delay (see for instance [11, 18, 22, 23]), the present work is, to the best of our knowledge, the first one which uses it to characterize a robustness property of a PDE.”
Approximately bisimilar symbolic models for nonlinear control systems (2007, neutral): “ms, conditions of Theorems 4.2 and 5.1 simplify. In fact given a linear control system: x˙ = Ax+Bu, x∈ Rn, u∈ U⊆ Rm, notions of δ–GAS and δ–ISS reduce to asymptotic stability of matrix A; moreover by [20], functions βand γ appearing in inequalities (2.1) and (2.2) can be chosen as: β(r,s) = keAskr; ”
Decentralized Event-Triggered Control Over Wireless Sensor/Actuator Networks (2010, neutral): “Let us start by considering a nonlinear control system: and assume that a feedback control law k : R n → R m , υ = k ( ξ ) is available, rendering the closed-loop system: input-to-state stable (ISS) [24] with respect to measurement errors ε : R +0 → R n .”
Homogeneous Approximation, Recursive Observer Design, and Output Feedback (2008, background): “A direct consequence of this result is an Inputto-State Stability (ISS) property with respect to disturbances (see [31]).”
Input-to-State Safety With Control Barrier Functions (2018, background): “nctions via sum of squares [7], and especially, robustness analysis via the notion of inputto-state safety (ISSf) [9]. Input-to-state safety (ISSf) is the equivalent of input-to-state stability (ISS) [12], an elegant theory used to characterize stability of nonlinear systems under input disturbances”