Dissipative filtering for two-dimensional LPV systems: A hidden Markov model approach.

Area of Science:

• Control Systems Engineering
• Systems Theory
• Signal Processing

Background:

• Addresses the challenge of dissipative filtering for complex 2-D Markov jump linear parameter varying (MJLPV) systems.
• Incorporates the Fornasini-Marchesini (FM) model and accounts for the common issue of missing measurements.
• Utilizes a Hidden Markov Model (HMM) to represent the partial accessibility between system and filter modes.

Purpose of the Study:

• To develop and analyze a novel HMM-based filter for 2-D MJLPV systems with missing measurements.
• To establish sufficient conditions for asymptotic stability (AS) and strict dissipativity of the filtering error system (FES).
• To convert the filter synthesis into a solvable convex optimization problem.

Main Methods:

• Design of a Hidden Markov Model (HMM)-based filter.
• Derivation of sufficient conditions using parameterized linear matrix inequalities (PLMIs).
• Formulation of the filter synthesis as a convex optimization problem.

Main Results:

• Sufficient conditions are established to guarantee asymptotic stability (AS) and strict dissipativity for the filtering error system (FES).
• The proposed filter design is shown to be effective through a simulation example.
• The filter synthesis problem is successfully converted into a convex optimization problem.

Conclusions:

• The developed HMM-based filter effectively addresses the dissipative filtering problem for 2-D MJLPV systems with missing measurements.
• The proposed method provides a systematic approach to designing stable and dissipative filters for such systems.
• Simulation results validate the practical utility and performance of the proposed filtering technique.