NDLI: Stability radius formulation of L σ-gain in positive stabilisation of regular and time-delay systems

Content Provider	IET Digital Library
Author	Shafai, Bahram Naghnaeian, Mohammad Chen, Jie
Abstract	This study initially considers the relationship between stability radius and L σ -gain of linear time-invariant positive systems. The L 1 -, L 2 -, and L ∞ -gains of an asymptotically stable positive system are characterised in terms of stability radii and useful bounds are derived. The authors show that the structured perturbation of a stable matrix can be regarded as a closed-loop system with uncertainty structure represented by the unknown static output feedback. This makes it possible to relate the L σ -gains in terms of closed-form expression available for stability radii of Metzler matrices. The authors generalise the above connection for positive-delay systems as well. Performance characterisation and computation of L σ -gains are also given based on linear programming for σ = 1 , ∞ and linear matrix inequality (LMI) for σ = 2 . The importance of this characterisation becomes evident when state feedback controllers are designed for regular and time-delay systems with positivity constraints. In particular, they show that positive stabilisation with maximum stability radius for the case of σ = 2 can be considered as an L 2 -gain minimisation, which can be solved by LMI. This inherently achieves the performance criterion and establishes a link to the reported iterative convex optimisation approaches that have been developed for the cases of σ = 1 and σ = ∞ . A significant result of this study is the derivation of bounds for L σ -gains and the unique commonality among the optimal state feedback gain matrices in obtaining L σ -gains of the stabilised system.
Starting Page	2327
Ending Page	2335
Page Count	9
ISSN	17518644
Volume Number	13
e-ISSN	17518652
Issue Number	Issue 15, Oct (2019)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-cta/13/15
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-cta.2018.5296
Journal	IET Control Theory & Applications
Publisher Date	2019-06-13
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Algebra Asymptotic Stability Asymptotically Stable Positive System Closed Loop System Closed-loop System Continuous Time System Control System Analysis Control System Synthesis Convex Programming Delay Delay System Distributed Parameter Control System Gain Minimisation Interpolation And Function Approximation Iterative Method Linear Matrix Inequalities Linear Matrix Inequality Linear Programming Linear System Linear Time-invariant Positive System Maximum Stability Radius Numerical Analysis Optimal State Feedback Gain Matrix Optimisation Technique Positive Stabilisation Positive-delay System Positivity Constraint Stabilised System Stability in Control Theory Stability Radii Stability Radius Formulation State Feedback State Feedback Controller Structured Perturbation Synthesis Method Time Varying Control System Time Varying System Time-delay System Uncertain System Uncertainty Structure Unknown Static Output Feedback
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Human-Computer Interaction Electrical and Electronic Engineering Computer Science Applications

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