Robust PI Controller Design for Positive Systems

TL;DR: This paper proposes a bumpless transfer PID control for discrete-time switched positive systems, ensuring positivity, stability, and bumpless transfer performance under synchronous and asynchronous switching via a matrix decomposition approach and copositive Lyapunov function.

TL;DR: In this paper , the authors proposed an event-triggered proportional integral (PI) controller design for positive switched systems in both continuous and discrete-time cases, which can guarantee the positivity and stability of the original systems.

TL;DR: In this article , the authors proposed an event-triggered proportional integral (PI) controller design for positive switched systems in both continuous and discrete-time cases, which can guarantee the positivity and stability of the original systems.

Abstract: This paper is devoted to robust gain scheduled PID controller design with L 2 performance for the linear time varying (LPV) uncertain system with polytopic uncertainties. The novel approach of robust controller design ensures that the obtained design procedure is convex with respect to both plant uncertainties (polytopic system) and gain scheduling parameters and gives less conservative results. Modified design procedure should be used to obtain a robust controller or robust switched controller (ideal, non-ideal switching) with arbitrarily switching algorithm. The effectiveness of the proposed approach is illustrated on the simulation examples.

TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.

TL;DR: Free MATLAB toolbox YALMIP is introduced, developed initially to model SDPs and solve these by interfacing eternal solvers by making development of optimization problems in general, and control oriented SDP problems in particular, extremely simple.

TL;DR: In this article, the authors define and define conditions of positivity of equilibria, including reachability and observability, and define a set of conditions for positive equilibrium. But they do not define the conditions of transparency.

TL;DR: Elements of Probability Theory Uncertain Linear Systems and Robustness Linear Robust Control Design Some Limits of the Robusts Paradigm Probabilistic Methods for Robustity Monte Carlo Methods Randomized Algorithms in Systems and Control Probability Inequalities Statistical Learning Theory and Control Design Sequential Al algorithms for probabilistic Robust design SequentialAlgorithms for LPV Systems Scenario approach.