815 research outputs found
Stability analysis of a general class of singularly perturbed linear hybrid systems
Motivated by a real problem in steel production, we introduce and analyze a
general class of singularly perturbed linear hybrid systems with both switches
and impulses, in which the slow or fast nature of the variables can be
mode-dependent. This means that, at switching instants, some of the slow
variables can become fast and vice-versa. Firstly, we show that using a
mode-dependent variable reordering we can rewrite this class of systems in a
form in which the variables preserve their nature over time. Secondly, we
establish, through singular perturbation techniques, an upper bound on the
minimum dwell-time ensuring the overall system's stability. Remarkably, this
bound is the sum of two terms. The first term corresponds to an upper bound on
the minimum dwell-time ensuring the stability of the reduced order linear
hybrid system describing the slow dynamics. The order of magnitude of the
second term is determined by that of the parameter defining the ratio between
the two time-scales of the singularly perturbed system. We show that the
proposed framework can also take into account the change of dimension of the
state vector at switching instants. Numerical illustrations complete our study
Analysis, estimation and control for perturbed and singular systems and for systems subject to discrete events.
Investigators: Alan S. Willsky, George Verghese.Annual technical report for Grant AFOSR-88-0032.Sponsored by the AFOSR. AFOSR-88-003
Stability of gain scheduling control for aircraft with highly nonlinear behavior
"The main goal of this work is to study the stability properties of an aircraft with nonlinear behavior, controlled using a gain scheduled approach. An output feedback is proposed which is able to guarantee asymptotical stability of the task-coordinates origin and safety of the operation in the entire flight envelope. The results are derived using theory of hybrid and singular perturbed systems. It is demonstrated that both body velocity and orientation asymptotic tracking can be obtained in spite of nonlinearities and uncertainty. The results are illustrated using numerical simulations in F16 jet.
Anti‐windup controller design for singularly perturbed systems subject to actuator saturation
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/166157/1/cth2bf00153.pd
34th Midwest Symposium on Circuits and Systems-Final Program
Organized by the Naval Postgraduate School Monterey California. Cosponsored by the IEEE Circuits and Systems Society.
Symposium Organizing Committee: General Chairman-Sherif Michael, Technical Program-Roberto Cristi, Publications-Michael Soderstrand, Special Sessions- Charles W. Therrien, Publicity: Jeffrey Burl, Finance: Ralph Hippenstiel, and Local Arrangements: Barbara Cristi
Singularly Perturbed Stochastic Hybrid Systems: Stability and Recurrence via Composite Nonsmooth Foster Functions
We introduce new sufficient conditions for verifying stability and recurrence
properties in singularly perturbed stochastic hybrid dynamical systems.
Specifically, we focus on hybrid systems with deterministic continuous-time
dynamics that exhibit multiple time scales and are modeled by constrained
differential inclusions, as well as discrete-time dynamics modeled by
constrained difference inclusions with random inputs. By assuming regularity
and causality of the dynamics and their solutions, respectively, we propose a
suitable class of composite nonsmooth Lagrange-Foster and Lyapunov-Foster
functions that can certify stability and recurrence using simpler functions
related to the slow and fast dynamics of the system. We establish the stability
properties with respect to compact sets, while the recurrence properties are
studied only for open sets
Stability of Hybrid Singularly Perturbed Systems with Time Delay
Hybrid singularly perturbed systems (SPSs) with time delay are considered and exponential stability of these systems is investigated. This work mainly covers switched and impulsive switched delay SPSs . Multiple Lyapunov functions technique as a tool is applied to these systems. Dwell and average dwell time approaches are used to organize the switching between subsystems (modes) so that the hybrid system is stable. Systems with all stable modes are first discussed and, after developing lemmas to ensure existence of growth rates of unstable modes, these systems are then extended to include, in addition, unstable modes. Sufficient conditions showing that impulses contribute to yield stability properties of impulsive switched systems that consist of all unstable subsystems are also established. A number of illustrative examples are presented to help motivate the study of these systems
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