Finite-time stability is defined for equilibria of continuous but non-Lipschitzian autonomous systems. Continuity, Lipschitz continuity, and Hölder continuity the settling-time function are studied illustrated with several examples. Lyapunov converse results involving scalar differential inequalities given finite-time stability. It shown that regularity properties those related. Consequently, can only assure existence functions. Finally, sensitivity finite-time-stable systems to...

A class of bounded continuous time-invariant finite-time stabilizing feedback laws is given for the double integrator. Lyapunov theory used to prove convergence. For rotational integrator, these controllers are modified obtain finite-time-stabilizing that avoid "unwinding".

An LQG (linear quadratic Gaussian) control-design problem involving a constraint on H/sup infinity / disturbance attenuation is considered. The performance embedded within the optimization process by replacing covariance Lyapunov equation Riccati whose solution leads to an upper bound L/sub 2/ performance. In contrast pair of separated equations standard theory, /-constrained gains are given coupled system three modified equations. coupling illustrates breakdown separation principle for...

Examines finite-time stability of homogeneous systems. The main result is that a system stable if and only it asymptotically has negative degree homogeneity.

First-order necessary conditions for quadratically optimal, steady-state,fixed-order dynamic compensation of a linear, time-invariant plant in the presence disturbance and observation noise are derived new highly simplified form. In contrast to pair matrix Riccati equations full-order LQG case, optimal steady-state fixed-order compensator is characterized by four (two modified two Lyapunov equations) coupled projection whose rank precisely equal order which determines gains. The coupling...

Abstract The purpose of this paper is to construct Lyapunov functions prove the key fundamental results linear system theory, namely, small gain (bounded real), positivity (positive circle, and Popov theorems. For each result a suitable Riccati‐like matrix equation used explicitly function that guarantees asymptotic stability feedback interconnection time‐invariant memoryless nonlinearity. for are also constructed two transfer functions. A multivariable version circle criterion, which yields...

The classical Duhem model provides a finite-dimensional differential of hysteresis. In this paper, we consider rate-independent and rate-dependent semilinear models with provable properties. vector field is given by the product function input rate linear dynamics. If positively homogeneous, then resulting input-output map independent, yielding persistent nontrivial closed curve (that is, hysteresis) at arbitrarily low frequency. not dependent can be approximated for frequency inputs....

First-order necessary conditions for quadratically optimal reduced-order modeling of linear time-invariant systems are derived in the form a pair modified Lyapunov equations coupled by an oblique projection which determines model. This considerably simplifies previous results Wilson [1] and clearly demonstrates quadratic extremality nonoptimality balancing method Moore [2]. The possible existence multiple solutions is demonstrated relaxation-type algorithm proposed computing these local...

The purpose of this article is to illuminate the critical role system zeros in control-system performance for benefit a wide audience both inside and outside control systems community. Zeros are fundamental aspect theory; however, causes effects more subtle than those poles. In particular, positive can cause initial undershoot (initial error growth), zero crossings, overshoot step response system, whereas nonminimum-phase limit bandwidth. Both these aspects have real-world implications many...

A design procedure is developed that combines linear-quadratic optimal control with regional pole placement. Specifically, a static and dynamic output-feedback problem addressed in which the poles of closed-loop system are constrained to lie specified regions complex plane. These constraints embedded within optimization process by replacing covariance Lyapunov equation modified whose solution, certain cases, leads an upper bound on quadratic cost functional. The results include necessary...

We derive a continuous nonlinear control law for spacecraft attitude tracking of arbitrary continuously differentiable trajectories based on rotation matrices.This formulation provides almost global stabilizability, that is, Lyapunov stability the desired equilibrium error system as well convergence from all initial states except subset which complement is open and dense.This controller thus overcomes unwinding phenomenon associated with controllers representations, such quaternions, are not...

In this paper we described the ensemble Kalman filter algorithm. This approach to nonlinear filtering is a Monte Carlo procedure, which has been widely used in weather forecasting applications. Our goal was apply representative examples quantify tradeoff between estimation accuracy and size. For all of linear that considered, worked successfully once threshold size reached. future work will investigate factors determine value.

We design an adaptive controller for a quadrotor UAV transporting point-mass payload connected by flexible cable modeled as serially-connected rigid links. The mass of the is uncertain. objective to transport desired position while aligning links along vertical direction from arbitrary initial condition. A fixed-gain nonlinear proportional-derivative presented achieve performance nominal mass, and retrospective cost used compensate uncertainty.

Recursive least squares (RLS) is a technique used for minimizing quadratic cost function, where the minimizer updated at each step as new data become available. RLS more computationally efficient than batch squares, and it extensively system identification adaptive control. This article derives emphasizes its real-time implementation in terms of availability well time needed computation.

This work presents generalized forgetting recursive least squares (GF-RLS), a generalization of (RLS) that encompasses many extensions RLS as special cases. First, sufficient conditions are presented for the 1) Lyapunov stability, 2) uniform 3) global asymptotic and 4) exponential stability parameter estimation error in GF-RLS when estimating fixed parameters without noise. Second, robustness guarantees derived timevarying presence measurement noise regressor These terms ultimate boundedness...