Abstract
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.
Highlights
Quadratic Stabilization of LinearPositive systems cover a special family of systems possessing the property that their states and outputs are inherently non-negative and, as a consequence, are subconsciously connected with such real processes whose internal variables are positive [1,2]
Can be used to control the uncertainty-free positive system (1) the problem is, with respect to diagonal stabilization principle, to formulate the set of linear matrix inequalities (LMIs), which guarantees, in a feasible case, a K ∈ Rr+×n being positive if the matrix variable P ∈ Rn+×n is positive definite diagonal
The design condition are derived from the corresponding algorithms for representations of feasible sets of LMIs, a representative of such an equivalence LMI corresponds to a certain choice of positive definite diagonal LMI variables, as a basis for diagonal stabilization
Summary
Positive systems cover a special family of systems possessing the property that their states and outputs are inherently non-negative and, as a consequence, are subconsciously connected with such real processes whose internal variables are positive [1,2]. New design conditions are derived related to uncertain discrete-time systems, which ensure both quadratic stability and positiveness performances in controller and observer. The multi-input, multi-output (MIMO) state-space representation is preferred, because the performance specifications used in the design task have to view the controller-related dimensions of matrix parameters when defining the uncertainties by LMIs. Because the objective is intended for diagonal positive matrix variables, it guarantees the diagonal stabilization principle. For clarity of presentation, following the decisive reason for preference given, the paper continues in Section 2 with separate treatments of the design fundamentals related to constraint formulations for uncertain positive discrete-time linear systems. ) means the set of strictly (purely) positive square matrices, respectively
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
