Analysis of Non-Monotonic Piecewise Lyapunov Stability and Semi-PID Design for Multi-Input Multi-Output Piecewise Affine Systems

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Solgi Younes

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Journal Paper

Paper Information

Journal: International Journal of Research and Technology in Electrical Industry Year:2024 | Volume:3 | Issue:2 Page(s): 391-401

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Information Journal Paper

Title

Analysis of Non-Monotonic Piecewise Lyapunov Stability and Semi-PID Design for Multi-Input Multi-Output Piecewise Affine Systems

Author(s)

Solgi Younes | Issue Writer Certificate

Keywords

Piecewise Affine Systems

Lyapunov-based stability

Linear Matrix Inequality

Non-Monotonic Lyapunov Theorem

PID Controller

Abstract

In this study, we introduce the Non-monotonic Lyapunov (NML) approach, aimed at stability examining and designing stabilizable controller for a specific category of discrete piecewise affine dynamical systems. Traditional Lyapunov techniques are often characterized by their conservative nature, which has spurred the creation of more adaptable methods like NML. A key distinction of the NML approach is its lack of reliance on strict monotonicity when establishing the decrease of a Lyapunov functional. As a result, we derive new stability and stabilization criteria based on the NML framework, expressed as LMIs (linear matrix inequalities) tailored for Piecewise Affine Systems. This NML-based methodology is employed to develop a semi-PID controller which is also able to handle multi-input multi-output (MIMO) piecewise linear systems. Additionally, we present an algorithm for optimal semi-PID controller design, aimed at achieving both optimal trajectories and refined control signals. The effectiveness of this innovative approach is highlighted through various examples and simulation results, demonstrating its significant contributions to PID design within complex systems. The findings underscore the practical applicability and advantages of the NML method in enhancing control strategies.

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