Geometric methods in linearization of control systems
Global linearization of nonlinear systems - A survey
A survey of the global linearization problem is presented. Known results are divided into two groups: results for general affine nonlinear systems and for bilinear systems. In the latter case stronger results are available. A comparision of various linearizing transformations is performed. Numerous illustrative examples are included.
Infinite elementary divisor structure-preserving transformations for polynomial matrices
The main purpose of this work is to propose new notions of equivalence between polynomial matrices that preserve both the finite and infinite elementary divisor structures. The approach we use is twofold: (a) the 'homogeneous polynomial matrix approach', where in place of the polynomial matrices we study their homogeneous polynomial matrix forms and use 2-D equivalence transformations in order to preserve their elementary divisor structure, and (b) the 'polynomial matrix approach', where some conditions...
Infinitesimal Brunovský form for nonlinear systems with applications to Dynamic Linearization
We define, in an infinite-dimensional differential geometric framework, the 'infinitesimal Brunovský form' which we previously introduced in another framework and link it with equivalence via diffeomorphism to a linear system, which is the same as linearizability by 'endogenous dynamic feedback'.
Input constraints handling in an MPC/feedback linearization scheme
The combination of model predictive control based on linear models (MPC) with feedback linearization (FL) has attracted interest for a number of years, giving rise to MPC+FL control schemes. An important advantage of such schemes is that feedback linearizable plants can be controlled with a linear predictive controller with a fixed model. Handling input constraints within such schemes is difficult since simple bound contraints on the input become state dependent because of the nonlinear transformation...
Invariant measures and controllability of finite systems on compact manifolds
A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.
Invariant measures and controllability of finite systems on compact manifolds
A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.
Invariant measures and controllability of finite systems on compact manifolds
A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.
Invariants and canonical forms for linear multivariable systems under the action of orthogonal transformation groups
Jacobi type conditions for singular extremals
New coprime polynomial fraction representation of transfer function matrix
A new form of the coprime polynomial fraction of a transfer function matrix is presented where the polynomial matrices and have the form of a matrix (or generalized matrix) polynomials with the structure defined directly by the controllability characteristics of a state- space model and Markov matrices , , ...
Notes on a hierarchical theory of systems and applications
On dynamic feedback linearization of four-dimensional affine control systems with two inputs
On dynamic feedback linearization of four-dimensional affine control systems with two inputs
This paper considers control affine systems in with two inputs, and gives necessary and sufficient conditions for dynamic feedback linearization of these systems with the restriction that the "linearizing outputs" must be some functions of the original state and inputs only. This also gives conditions for non-affine systems in .
On obtaining the time-invariant associated system of a periodic system through system equivalence
On the bounded input-bounded output stability of a second-order linear difference equation
On the decentralized stabilization of interconnected discrete time systems
On various dynamic compensations
Partial decoupling of non-minimum phase systems by constant state feedback
Periodic systems largely system equivalent to periodic discrete-time processes
In this paper, the problem of obtaining a periodic model in state-space form of a linear process that can be modeled by linear difference equations with periodic coefficients is considered. Such a problem was already studied and solved in [r71] on the basis of the notion of system equivalence, but under the assumption that the process has no null characteristic multiplier. In this paper such an assumption is removed in order to generalize the results in [r71] to linear periodic processes with possibly...