Stability radii of positive discrete‐time systems under affine parameter perturbations (original) (raw)
Related papers
Stability Radii of Positive Discrete-Time Systems
1994
In this paper we study stability radii of positive linear discrete-time systems under a ne parameter perturbations. It is shown that real and complex stability radii of positive systems coincide for arbitrary perturbation structures, in particular for blockdiagonal disturbances as considered in -analysis. Estimates and computable formulae are derived for these stability radii. The results are derived for arbitrary perturbation norms induced by monotonic vector norms (e.g. p-norms, 1 p 1).
Positivity, 2008
In this paper we study the stability radii of positive linear discrete system under arbitrary affine parameter perturbations in infinite dimensional spaces. It is shown that complex, real, and positive stability radii of positive systems coincide. More importantly, estimates and computable formulas of these stability radii are also derived. The results are then illustrated by a simple example. The obtained results are extensions of the recent results in [3].
Stability radii of positive linear difference equations under affine parameter perturbations
Applied Mathematics and Computation, 2003
In this paper we study stability radii of positive linear difference equations under arbitrary affine parameter perturbations. It is shown that real and complex stability radii of positive equations coincide for block-diagonal disturbances. Moreover, for these stability radii, estimates and computable formulae are derived which generalize to positive linear difference equations known results obtained earlier for positive linear discrete-time systems of the form x(k+1)=Ax(k), . Some illustrative examples are given.
Stability radii of higher order positive difference systems
Systems & Control Letters, 2003
In this paper we study stability radii of positive polynomial matrices under affine perturbations of the coefficient matrices. It is shown that the real and complex stability radii coincide. Moreover, explicit formulas are derived for these stability radii and illustrated by some examples.
Quadratic Stabilization of Linear Uncertain Positive Discrete-Time Systems
Symmetry, 2021
The paper provides extended methods for control linear positive discrete-time systems that are subject to parameter uncertainties, reflecting structural system parameter constraints and positive system properties when solving the problem of system quadratic stability. By using an extension of the Lyapunov approach, system quadratic stability is presented to become apparent in pre-existing positivity constraints in the design of feedback control. The approach prefers constraints representation in the form of linear matrix inequalities, reflects the diagonal stabilization principle in order to apply to positive systems the idea of matrix parameter positivity, applies observer-based linear state control to assert closed-loop system quadratic stability and projects design conditions, allowing minimization of an undesirable impact on matching parameter uncertainties. The method is utilised in numerical examples to illustrate the technique when applying the above strategy.
Stability radii of positive linear systems under fractional perturbations
International Journal of Robust and Nonlinear Control, 2009
In this paper we study stability radii of positive linear discrete-time systems under fractional perturbations. It is shown that real and complex stability radii coincide and can be computed by a simple formula. From the obtained results, we apply to derive estimates and computable formulae for the stability radii of positive linear delay systems. Finally, a simple example is given to illustrate the obtained results.
On robust stability of positive differentiable linear systems
… and Control, 1995., Proceedings of the …, 1995
In this note a simple formula for the real stability radius of uncertain positive linear systems is established and it is shown that the real stability radius coincides with the complex one. Arbitrary disturbance norms induced by monotonic vector norms (e.g. pnorms, 1 ≤ p ≤ ∞) are considered. The distance of intervals of positive systems from instability is also determined.
Stabilization of discrete-time LTI positive systems
Archives of Control Sciences
The paper mitigates the existing conditions reported in the previous literature for control design of discrete-time linear positive systems. Incorporating an associated structure of linear matrix inequalities, combined with the Lyapunov inequality guaranteing asymptotic stability of discrete-time positive system structures, new conditions are presented with which the state-feedback controllers and the system state observers can be designed. Associated solutions of the proposed design conditions are illustrated by numerical illustrative examples.
Robust stability and transient behaviour of positive linear systems
2000
After a brief review of available results the main focus of the paper is on the tran- sient behaviour of positive systems and their stability radii with respect to highly structured perturbations. Simple upper bounds for the transient gain of positive systems are obtained by means of linear Lyapunov functions on the positive or- thant. The minimization of these bounds