Model reduction for the descriptor systems by linear matrix inequalities

2010 ◽  
Vol 8 (4) ◽  
pp. 875-881 ◽  
Author(s):  
Do-Chang Oh ◽  
Eun-Tae Jeung
Keyword(s):  
Model Reduction ◽  
Linear Matrix Inequalities ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Matrix Inequalities

scholarly journals Finite frequency model reduction for 2-D fuzzy systems in FM model

2021 ◽  
Vol 297 ◽  
pp. 01035
Author(s):  
Rachid Naoual ◽  
Abderrahim El-Amrani ◽  
Ismail Boumhidi
Keyword(s):  
Model Reduction ◽  
State Space ◽  
Linear Matrix Inequalities ◽  
Fuzzy Systems ◽  
Linear Matrix ◽  
Two Dimensional ◽  
Matrix Inequalities ◽  
Finite Frequency ◽  
Frequency Model ◽  
Takagi Sugeno

This paper deals with the problem of H∞ model reduction for two-dimensional (2D) discrete Takagi-Sugeno (T-S) fuzzy systems described by Fornasini-Marchesini local state-space (FM LSS) models, over finite frequency (FF) domain. New design conditions guaranteeing the FF H∞ model reduction are established in terms of Linear Matrix Inequalities (LMIs). To highlight the effectiveness of the proposed H∞ model reduction design, a numerical example is given.

scholarly journals Robust Finite-TimeH∞Control for Linear Time-Varying Descriptor Systems with Jumps

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Xiaoming Su ◽  
Adiya Bao
Keyword(s):  
Linear Matrix Inequalities ◽  
Finite Time ◽  
Linear Time ◽  
Descriptor Systems ◽  
Feasibility Problem ◽  
Descriptor System ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Finite Time Boundedness

The finite-timeH∞control problem is addressed for uncertain time-varying descriptor system with finite jumps and time-varying norm-bounded disturbance. Firstly, a sufficient condition of finite-time boundedness for the abovementioned class of system is obtained. Then the result is extended to finite-timeH∞for the system. Based on the condition, state feedback controller is designed such that the closed-loop system is finite-time boundedness and satisfiesL2gain. The conditions are given in terms of differential linear matrix inequalities (DLMIs) and linear matrix inequalities (LMIs), and such conditions require the solution of a feasibility problem involving DLMIs and LMIs, which can be solved by using existing linear algorithms. Finally, a numerical example is given to illustrate the effectiveness of the method.

scholarly journals Quantized Dissipative Observer-Based Output Feedback Control for a Class of Markovian Descriptor Jump Systems with Communication Delay

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Muhammad Shamrooz Aslam ◽  
Xisheng Dai
Keyword(s):  
Feedback Control ◽  
Linear Matrix Inequalities ◽  
Output Feedback ◽  
Nonlinear Dynamical Systems ◽  
Output Feedback Control ◽  
Descriptor Systems ◽  
Space Representation ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Jump Systems

This paper investigates the problem of quantized dissipative observer-based output feedback control of Markovian descriptor jump systems with unavailable states, appearing networked-induced delay. The descriptor systems are presented as Markovian jump systems which give a more realistic presentation for a variety of nonlinear dynamical systems than conventional state-space representation. To accomplish the objective, a uniform framework is employed to design the delayed Markov observer-based controller and event-triggered scheme. Additionally, we provided the ℋ∞ and ℒ2-ℒ∞ and dissipative performance indices which are robust against the disturbances with time-varying delays. Moreover, a novel Lyapunov–Krasovskii functional is considered to guarantee the closed loop for stochastic stability analysis of the Markovian descriptor jump system. The solvability of Lyapunov–Krasovskii functional results in the formation of linear matrix inequalities. The controller and observer gains can be obtained by solving the linear matrix inequalities. Simulations are performed to validate the proposed scheme.

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