New conditions for finite-time stability of impulsive dynamical systems via piecewise quadratic functions

In this paper, the use of time-varying piecewise quadratic functions is investigated to characterize the finite-time stability of state-dependent impulsive dynamical linear systems. Finite-time stability defines the behavior of a dynamic system over a bounded time interval. More precisely, a system is said to be finite-time stable if, given a set of initial conditions, its state vector does not exit a predefined domain for a certain finite interval of time. This paper presents new sufficient conditions for finite-time stability based on time-varying piecewise quadratic functions. These conditions can be reformulated as a set of Linear Matrix Inequalities that can be efficiently solved through convex optimization solvers. Dif ferent numerical analysis are included in order to prove that the presented conditions are able to improve the results presented so far in the literature

Dynamics of interconnected systems with pulse frequency modulators

The objective of this dissertation is to study the dynamics of systems consisting of interconnections of an arbitrary number of complete-reset pulse frequency modulators (CRPFM\u27s) and linear dynamical subsystems (in general, time-varying, lumped and/or distributed). CRPFM, which represents a generalization of several types of pulse frequency modulators (PFM\u27s), consists of two basic components; a multi-input dynamic element, called the timing-filter (TF) and a threshold device (TD). Whenever the output of the TF reaches a given threshold value the TD generates an impulse and, at the same time, resets all the states of the TF to zero. This dissertation is devoted to two basic aspects of system motion, namely stability of the equilibrium and periodic operation. Stability is defined in terms of finiteness of the number of pulses emitted by all modulators. This definition of finite-pulse stability (FPS) is related to L1 ∩ LP output stability and implies finite energy expended. An improved Lyapunov-like approach is presented which, however, is difficult to employ for higher order systems. A direct criterion for FPS is given which is not only easy to apply, but also provides bounds on the number of pulses emitted by each modulator. A comparison is presented between these criteria and previous stability conditions available for special classes of CRPFM systems (e.g., systems with integral PFM or relaxation PFM). In representative examples, the direct FPS criterion yields comparable (or better) stability regions (of parameters). The second part is devoted to the study of the basic aspects of periodic behavior. For multi-modulator PFM systems, the usual concept of periodicity (or almost periodicty) is not meaningful. Therefore, a weaker concept, that of εe-near periodicity is introduced. This notion involves an observation interval (which is usually finite) and a measure of desired accuracy or observation accuracy . Certain necessary and sufficient conditions for the existence of εe-near periodic motion are presented. For an IPFM system with a time-invariant linear part, a matrix relationship is given, which relates the period and the net number of pulses emitted by each modulator over that period to the system parameters. Periodic behavior is further investigated on a time-discretized approximation of the CRPFM system which reduces to a system containing ideal delays, summing junctions and threshold elements. However, it is still difficult to obtain analytical results from the resulting (nonlinear) difference equations (except for very short periods of oscillation); nevertheless, these equations can be linearized by introduction of extra variables, using Fukunaga\u27s method for nonlinear switching nets. Therefore, classical linear techniques (based on characteristic polynomials and eigenvectors) can be used to obtain information about periodic motion. This approach also applies to McCulloch Pitts type of neural nets and extends existing results on periodic behavior in such networks

Robust Stability Analysis of Nonlinear Hybrid Systems

We present a methodology for robust stability analysis of nonlinear hybrid systems, through the algorithmic construction of polynomial and piecewise polynomial Lyapunov-like functions using convex optimization and in particular the sum of squares decomposition of multivariate polynomials. Several improvements compared to previous approaches are discussed, such as treating in a unified way polynomial switching surfaces and robust stability analysis for nonlinear hybrid systems

Robust fault detection for vehicle lateral dynamics: Azonotope-based set-membership approach

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksIn this work, a model-based fault detection layoutfor vehicle lateral dynamics system is presented. The majorfocus in this study is on the handling of model uncertainties andunknown inputs. In fact, the vehicle lateral model is affectedby several parameter variations such as longitudinal velocity,cornering stiffnesses coefficients and unknown inputs like windgust disturbances. Cornering stiffness parameters variation isconsidered to be unknown but bounded with known compactset. Their effect is addressed by generating intervals for theresiduals based on the zonotope representation of all possiblevalues. The developed fault detection procedure has been testedusing real driving data acquired from a prototype vehicle.Index Terms— Robust fault detection, interval models,zonotopes, set-membership, switched uncertain systems, LMIs,input-to-state stability, arbitrary switching.Peer ReviewedPostprint (author's final draft