Robust state-feedback stabilization of an underactuated network of interconnected <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e242" altimg="si1.svg"><mml:mrow><mml:mi>n</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">+</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:math> hyperbolic PDE systems

Robust control of hyperbolic PDE systems

-This work concerns systems of quasi-linear first-order hyperbolic partial differential equations (PDEs) with uncertain variables and unmodeled dynamics. For systems with uncertain variables, the problem of complete elimination of the effect of uncertainty on the output via distributed feedback (uncertainty decoupling) is initially considered; a necessary and sufficient condition for its solvab...

Robust Stabilization of Nonlinear Systems by Discontinuous Dynamic State Feedback

In this paper, a discontinuous dynamic state feedback that robustly stabilizes affine in control uncertain nonlinear systems is proposed. The formulation is based on Hamilton-Jacobi-Isaacs partial differential equations with two boundary conditions. The resulting dynamic state feedback is then expressed in terms of the solution of the related PDE’s. An interesting feature is that the internal s...

Time-Invariant State Feedback Control Laws for a Special Form of Underactuated Nonlinear Systems Using Linear State Bisection

Linear state bisection is introduced as a new method to find time-invariant state feedback control laws for a special form of underactuated nonlinear systems. The specialty of the systems considered is that every unactuated state should be coupled with at least two directly actuated states. The basic idea is based on bisecting actuated states and using linear combinations with adjustable parame...

Stabilization of coupled linear heterodirectional hyperbolic PDE-ODE systems

Decentralized dynamic output feedback for robust stabilization of a class of nonlinear interconnected systems

The objective of this paper is to propose an approach to robust stabilization of systems which are composed of linear subsystems coupled by nonlinear time-varying interconnections satisfying quadratic constraints. The proposed algorithms, which are formulated within the convex optimization framework, employ linear dynamic feedback structure involving local Luenberger-type observers. It is also ...