Input-output decoupling with stability for Hamiltonian systems

The input-output decoupling problem with stability for Hamiltonian systems is treated using decoupling feedbacks, all of which make the system maximally unobservable. Using the fact that the dynamics of the maximal unobservable subsystem are again Hamiltonian, an easily checked condition for input-output decoupling with (critical) stability is deduced

Nonlinear model matching: a local solution and two worked examples

The model matching problem consists of designing a compensator for a given system, called the plant, in such a way that the resulting input-output behavior matches that of a prespecified model. In a recent paper it was shown that in case the model is decouplable by static state feedback and generic conditions on the plant are satisfied, the model matching problem is solvable around an equilibrium point if and only if it is solvable for the linearization of plant and model around the equilibrium point. In this paper this local solution will be presented and we will investigate the question to what extent we can use the feedback that solves the corresponding linear model matching problem in order to approximately solve the original nonlinear problem. This will be done by means of two examples: the double pendulum and a two-link robot arm with a flexible joint

Minimality of dynamic input-output decoupling for nonlinear systems

In this note we study the strong dynamic input-output decoupling problem for nonlinear systems. Using an algebraic theory for nonlinear control systems, we obtain for a dynamic input-output decouplable nonlinear system a compensator of minimal dimension that solves the decoupling problem

Local nonlinear model matching: from linearity to nonlinearity

The model matching problem consists of designing a compensator for a given system, called the plant, in such a way that the resulting input-output behaviour matches that of a prespecified model. In this paper a local solution of the nonlinear model matching problem is given for the case that the model is decouplable by static state feedback. The main theorem states that under generic conditions on the plant the problem is solvable around an equilibrium point if and only if it is solvable for the linearization of plant and model. The generic conditions are identified. They naturally appear in the solution of the dynamic input-output decoupling problem for the plant. The theory is illustrated by means of two examples

Local asymptotic stability of optimal steady states

This note provides a sufficient condition for steady states arising from economic optimal control models to be locally asymptotically stable. In particular, we show that if some submatrix of the matrix of eigenvectors of the corresponding Jacobian is invertible, the stable manifolds is locally y-parametrizable

Dynamic disturbance decoupling of nonlinear systems and linearization

In this paper we investigate the connections between the solvability of the dynamic disturbance decoupling problem with exponential stability (DDDPes) for a nonlinear system and the solvability of the same problem for its linearization around an equilibrium point. It is shown that under generic conditions the nonlinear DDDPes is solvable for a nonlinear system if and only if the static disturbance decoupling problem with stability (DDPs) is solvable for its linearization around an equilibrium point