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Showing 1 to 20 of 41 for “"Lyapunov functions"”.
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Almost Lyapunov functions
… dynamical system that verifies the classical Lyapunov criterion is globally asymptotically stable for the case when the Lyapunov function is strictly decreasing along the solution. We define an almost Lyapunov function to be a candidate Lyapunov function whose derivative with respect to time …
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Computation of Lyapunov functions and stability of interconnected systems
… we investigate the problems of computation of Lyapunov functions and stability analysis of interconnected systems. In Chapter 1, preliminary results about stability, definitions of Lyapunov functions and triangulations are presented. In order to analyse stability of interconnected systems in …
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Control and filtering of time-varying linear systems via parameter dependent Lyapunov functions
… in different instants of time (path dependent) Lyapunov functions were used to obtain the design conditions, as well as extra variables introduced by the Finsler's lemma. Design problems that take into account an H-infinity guaranteed cost were investigated, providing robustness with respect to …
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Approximate Explicit MPC and Closed-loop Stability: Analysis based on PWA Lyapunov Functions
… exploits suitable and possibly discontinuous PWA Lyapunov-like functions. The tool requires solving offline a linear programming problem. Moreover, the tool is able to compute an invariant set for the closed-loop system, as well as ultimate boundedness and input-to-state stability properties.
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Non-monotonic Lyapunov functions for stability of nonlinear and switched systems : theory and computation
Lyapunov's direct method, which is based on the existence of a scalar function of the state that decreases monotonically along trajectories, still serves as the primary tool for establishing stability of nonlinear systems. Since the main challenge in stability analysis based on Lyapunov theory is …
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Nonlinear and switched systems: Geometric motion planning, non-monotonic Lyapunov functions and input-to-state stability
… studied two approaches related to non-monotonic Lyapunov functions. More explicitly, the techniques of ""almost Lyapunov"" functions and higher order derivatives of Lyapunov functions -- which were used to study the stability of autonomous nonlinear systems in the literature -- are generalized to …
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Piecewise Linear Control Systems
… is investigated using piecewise quadratic Lyapunov functions. Piecewise quadratic Lyapunov functions are much more powerful than the commonly used quadratic Lyapunov functions. It is shown how piecewise quadratic Lyapunov functions can be computed via convex optimization in terms of linear …
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Lyapunovfunctions in epidemiological modeling
In this mini thesis, we study the application of Lyapunov functions in epidemiological modeling. The aim is to give an extensive discussion of Lyapunov functions, and use some specific classes of epidemiological models to demonstrate the construction of Lyapunov functions. The study begins with a …
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A Lyapunov-based small-gain theorem for interconnected switched systems
… defined to enable the construction of hybrid ISS Lyapunov functions. Apart from justifying the ISS property of their corresponding switched systems, these hybrid ISS Lyapunov functions are then combined to establish a Lyapunov-type small-gain condition which guarantees that the interconnected …
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Algebraic relaxations and hardness results in polynomial optimization and Lyapunov analysis
… on existence of polynomial and sum of squares Lyapunov functions. We present a globally asymptotically stable polynomial vector field with no polynomial Lyapunov function. We show via an explicit counterexample that if the degree of the polynomial Lyapunov function is fixed, then sos …
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Studies on Stability and Stabilization of Randomly Switched Systems
… characteristics. The method of multiple Lyapunov functions is employed in conjunction with some statistical properties of the switching signal for the analysis. The results apply to situations where traditional methods involving infinitesimal generators are difficult to apply, either due …
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Optimization of Lyapunov invariants in analysis and implementation of safety-critical software systems
… the development of a novel framework, based on Lyapunov invariants and convex optimization, for verification of various safety and performance specifications for software systems. The enabling elements of the framework for software analysis are: (i) dynamical system interpretation and modeling …
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Switched and hybrid systems with inputs: small-gain theorems, control with limited information, and topological entropy
… time of non-ISpS modes is short in proportion, Lyapunov-based small-gain theorems are established via hybrid system techniques. By augmenting each subsystem with a hybrid auxiliary timer that models the constraints on switching, we enable a construction of hybrid ISpS-Lyapunov functions, and …
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Stability in dynamical polysystems
… use of the theory of closed relations to study Lyapunov functions. Prolongations and absolute stability make the object of the last chapter.
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Learning Stabilizing Controllers for High-dimensional Unknown Systems and Networked Dynamical Systems
… To address the challenge, we develop (1) A Lyapunov-based guided exploration framework to learn stabilizing controllers for high-dimensional unknown systems; (2) A compositional neural certificate based on ISS (Input-to-State Stability) Lyapunov functions for finding decentralized …
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Optimization for control and planning of multi-contact dynamic motion
… an algorithm for discovering polynomial Lyapunov functions, where the system dynamics include impacts and friction. We leverage the measure differential inclusion representation of non-smooth contact mechanics to efficiently optimize over Lyapunov functions in multi-contact settings. …
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Decoupled Stability Analysis of Power Systems With Slow and Fast Dynamics
… On a higher hierarchy, a weighted sum of the Lyapunov functions of the decoupled slow and fast subsystems is used as a Lyapunov function for the original two-time-scale system, thus accounting for the effect of the small coupling terms. Two case studies confirm the improved accuracy of the …
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Analysis and Simulation for Homogeneous and Heterogeneous SIR Models
… model utilizing a graph-theoretic approach and Lyapunov functions. Numerical simulations confirm nonlinear incidence gives raise to rich dynamics such as synchronization and phase-lock oscillations.
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Mathematical Models and Stability Analysis of Cholera Dynamics
… Particularly, we incorporate the Volterra-Lyapunov matrix theory into Lyapunov functions to facilitate the analysis of the global endemic stability. Based on the previous cholera models, we propose a new and unified deterministic model which incorporates a general incidence rate and a …
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Multivariable Adaptive Control
… The major result is a method for construction of Lyapunov functions for a class of single-input systems. Stability in the sense of Lyapunov and exponential convergence are shown.
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