197,493 research outputs found
Stability of switched linear differential systems
We study the stability of switched systems where the dynamic modes are
described by systems of higher-order linear differential equations not
necessarily sharing the same state space. Concatenability of trajectories at
the switching instants is specified by gluing conditions, i.e. algebraic
conditions on the trajectories and their derivatives at the switching instant.
We provide sufficient conditions for stability based on LMIs for systems with
general gluing conditions. We also analyse the role of positive-realness in
providing sufficient polynomial-algebraic conditions for stability of two-modes
switched systems with special gluing conditions
Applications of Linear Co-positive Lyapunov Functions for Switched Linear Positive Systems
In this paper we review necessary and sufficient conditions for the existence of a common linear co-positive Lyapunov function for switched linear positive systems. Both the state dependent and arbitrary switching cases are considered and
a number of applications are presented
On switched Hamiltonian systems
In this paper we study the well-posedness and stability of a class of switched linear passive systems. Instrumental in our approach is the result, also of interest in its own right, that any linear passive input-state-output system with strictly positive storage function can be written as a port-Hamiltonian system
On the D-Stability of Linear and Nonlinear Positive Switched Systems
We present a number of results on D-stability
of positive switched systems. Different classes of linear and
nonlinear positive switched systems are considered and simple
conditions for D-stability of each class are presented
Essentially Negative News About Positive Systems
In this paper the discretisation of switched and non-switched linear positive systems using
Padé approximations is considered. Padé approximations to the matrix exponential
are sometimes used by control engineers for discretising continuous time systems and
for control system design. We observe that this method of approximation is not suited
for the discretisation of positive dynamic systems, for two key reasons. First, certain
types of Lyapunov stability are not, in general, preserved. Secondly, and more seriously,
positivity need not be preserved, even when stability is. Finally we present an alternative
approximation to the matrix exponential which preserves positivity, and linear and
quadratic stability
On positive-realness and Lyapunov functions for switched linear differential systems
We show new results about Lyapunov stability of switched linear differential systems (SLDS) using the concept ofpositive realness. The main results include stability conditions for a class of SLDS with augmented banks and the parametrization of families of asymptotically stable SLDS with three modes. Such conditions can be verified using LMIs that can be directly set up from the higher-order differential equations describing the mode
On the preservation of co-positive Lyapunov functions under Padé discretization for positive systems
In this paper the discretization of switched and
non-switched linear positive systems using Padé approximations
is considered. We show:
1) first order diagonal Padé approximation preserves both
linear and quadratic co-positive Lyapunov functions,
higher order transformations need an additional condition
on the sampling time1;
2) positivity need not be preserved even for arbitrarily small
sampling time for certain Padé approximations.
Sufficient conditions on the Padé approximations are given to
preserve positivity of the discrete-time system. Finally, some
examples are given to illustrate the efficacy of our results
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