Julio Solís-Daun

Linear systems with bounded inputs: global stabilization with eigenvalue placement

This work presents a technique for obtaining a bounded continuous feedback control function which stabilizes a linear system in a certain region. If the open-loop system has no eigenvalues with positive real part, the region of attraction of the resulting closed-loop system is all ℝn, i.e., the feedback control is a global stabilizer; otherwise, the region contains an invariant (‘cylindric-like’) set where the controller does not saturate. The proposed control is a linear-like feedback control with state-dependent gains. The gains become implicitly defined in terms of a nonlinear scalar equation. The control function coincides in an ellipsoidal neighbourhood of the origin with a linear feedback law which is a solution of a linear quadratic regulator problem. This design allows eigenvalue placement in a specified region.

Global Stabilization of Nonlinear Systems with Inputs Subject to Magnitude and Rate Bounds: A Parametric Optimization Approach

A bounded feedback control design approach is proposed for the global asymptotic stabilization of a class of nonlinear systems with stable free dynamics. The control inputs and their derivatives are constrained to take values on sets defined by a Cartesian product of

Global CLF Stabilization of Nonlinear Systems. Part I: A Geometric Approach---Compact Strictly Convex CVS

\eta

Global CLF Stabilization of Systems with Control Inputs Constrained to a Hyperbox

-dimensional closed balls

Stabilization of linear controllable systems by means of bounded continuous nonlinear feedback control

\mathcal{B}_{\mathbf{r}}^{\eta }(p)

On the Global CLF Stabilization of Systems with Polytopic Control Value Sets

, which are defined by means of a p-norm and a radius vector parameter

Semiglobal stabilization of linear systems using constrained controls: a parametric optimization approach

\mathbf{r}

Synthesis of positive controls for the global CLF stabilization of systems

. In order to derive the bounded control stabilizer, the resulting procedure implies that gains (as state-functions) are obtained from the solution to a set of c -parameterized nonlinear programming problems. In general, the resulting closed-loop system could be implicitly defined, i.e., consisting of a system of differential equations plus a set of nonlinear algebraic equations (required to compute the control). Special interest is focused on an important class of homogeneous systems that includes a class of globally asymptotically stabilizable systems by linear feedback and bilinear systems. For those systems, the problem of inputs subject to globally bounded rates is also addressed.

Global CLF stabilization for systems with compact convex control value sets

The aim of this paper is to design regular feedback controls for the global asymptotic stabilization (GAS) of affine control systems with compact (convex) control value sets (CVS)

Global CLF Stabilization of Nonlinear Systems. Part II: An Approximation Approach---Closed CVS

U\subset\mathbb{R}^{m}