Stabilization Of Nonlinear Cascaded Systems Research Articles

Trading the stability of finite zeros for global stabilization of nonlinear cascade systems

Analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a stable nonlinear system. It is shown that the instability of the zeros of the linear system can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the cascade interconnection term. Below this limit, global stabilization is achieved by smooth static-state feedback. Beyond this limit, various examples illustrate that controllability of the cascade may be lost, making it impossible to achieve large regions of attractions.

Stability of Perturbed Delay Differential Equations and Stabilization of Nonlinear Cascade Systems

In this paper the effect of bounded input perturbations on the stability of nonlinear globally asymptotically stable delay differential equations is analyzed. We investigate under which conditions global stability is preserved and if not, whether semiglobal stabilization is possible by controlling the size or shape of the perturbation. These results are used to study the stabilization of partially linear cascade systems with partial state feedback.

Global Stabilization of Nonlinear Cascade Systems: Limitations Imposed by Right Half Plane Zeros

This paper analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a stable nonlinear system. It is shown that the instability of the zeros of the linear system can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the interconnection term between the two parts of the cascade. Below this limit, global stabilization is achieved by smooth static state feedback. Beyond this limit, various examples illustrate that controllability of the cascade may be lost, making it impossible to achieve large regions of attractions.

Constructive Lyapunov stabilization of nonlinear cascade systems

We present a global stabilization procedure for nonlinear cascade and feedforward systems which extends the existing stabilization results. Our main tool is the construction of a Lyapunov function for a class of (globally stable) uncontrolled cascade systems. This construction serves as a basis for a recursive controller design for cascade and feedforward systems. We give conditions for continuous differentiability of the Lyapunov function and the resulting control law and propose methods for their exact and approximate computation.

Linear stabilization of nonlinear cascade systems

In this paper we consider the cascade connection of a nonlinear system and a system of integrators. Under suitable conditions we prove that if the nonlinear subsystem is stabilizable by means of a linear feedback, then a linear stabilizer exists for the overall system as well. In particular, we point out the role of the classical notion ofk-asymptotic stability.

Global stabilization of nonlinear cascade systems

We present sufficient conditions for the global stabilizability of two cascade connected nonlinear systems. These are based on general results concerning global asymptotic stability of triangular systems which are proved in the last section. For polynomial systems, in particular, the stabilizing feedback is given explicitly.