H∞ norm principle in residual filter design for discrete-time linear positive systems

2021

Symmetry

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For time-invariant Metzler linear MIMO systems, this paper proposes an original approach reflecting necessary matching conditions, specifically structural system constraints and necessary positiveness in solving the problem of MIMO PID control. Covering the matching conditions by the supporting structure of measurement, refining the controller and system parameter constraints and introducing enhanced equivalent system descriptions, the reformulated design task is consistent with PID control law parameter representation and is formulated as a linear matrix inequality feasibility problem. Characterization of the PID control law parameters is permitted to highlight dynamical properties of the closed-loop system and the structural influence of the control derivative gain value in the design step. For the first time, the paper comprehensively sets the synthesis standard for PID control of MIMO Metzler systems because others for the given task have not been created at present.

Section: Linear Metzler Systems Formalism and Control System Strategiesmentioning

confidence: 99%

“…To avoid additional structured variable's phenomena in the design conditions [19], it can be taken as…”

Section: Data Availability Statementmentioning

confidence: 99%

On PID Design Constraints in Relation to Control of Strictly Metzler Linear MIMO Systems

2021

Symmetry

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“…If the above conditions are feasible it yields (32) and the strictly positive K is constructed using (12). Proof.…”

Section: H ∞ Control Synthesismentioning

confidence: 99%

“…The paper presents an approach in state control synthesis for discrete-time positive systems within mixed H 2 /H ∞ norm formulation. Motivated by the ideas presented in [10]- [12] design is covered via extended set of LMIs with fixing of H 2 norm of closed-loop system transform matrix combined with bounded real lemma LMI structure. LMIbased approach, characterizing synthesis of con-trollers is computationally simple, efficient, applicable to square multiple input and multiple output (MIMO) systems for strictly positive discrete-time linear systems as well as for non-negative class of these systems.…”

Section: Introductionmentioning

confidence: 99%

Mixed H2/H∞ Control Synthesis for Discrete-time Linear Positive Systems using Enhanced Set of Linear Matrix Inequalities

Wseas Transactions on Systems and Control

2020

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This paper provides an idea, resulting from linear matrix inequality representation of parameter constraints of discrete-time linear positive systems, to formulate state-feedback synthesis for this class of systems. The design conditions are imposed to obtain control respecting existing strictly positivity or non-negativity in the system matrix description. Formulated as a linear matrix inequality feasibility problem it is reiterated that approach leads iteratively to estimation of norms of closed-loop system

“…Adaptation of the presented new points of view given on the control synthesis of linear positive discrete-time systems in [18,19], as well as their dissemination to positive systems with uncertain parameters, are the main issues of this paper. In considerable order of precedence is LMI formulation in parametric constraint prescription, together with the structural quadratic stability, to handle more general preference of arguments based on the Lyapunov method.…”

Section: Introductionmentioning

confidence: 99%

Quadratic Stabilization of Linear Uncertain Positive Discrete-Time Systems

2021

Symmetry

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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.