scholarly journals Analysis of Robust Stability for a Class of Stochastic Systems via Output Feedback: The LMI Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Xin-rong Cong ◽  
Long-suo Li
Keyword(s):  
Linear Matrix Inequality ◽  
Robust Stability ◽  
Output Feedback ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Convex Optimization Problem ◽  
Control Laws ◽  
The Stability ◽  
And Control

This paper investigates the robust stability for a class of stochastic systems with both state and control inputs. The problem of the robust stability is solved via static output feedback, and we convert the problem to a constrained convex optimization problem involving linear matrix inequality (LMI). We show how the proposed linear matrix inequality framework can be used to select a quadratic Lyapunov function. The control laws can be produced by assuming the stability of the systems. We verify that all controllers can robustly stabilize the corresponding system. Further, the numerical simulation results verify the theoretical analysis results.

scholarly journals Stability of Hybrid Stochastic Systems with Time-Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Pu Xing-cheng ◽  
Yuan Wei
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Time Delay ◽  
Linear Matrix Inequality ◽  
Hybrid Systems ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Hybrid Stochastic Systems ◽  
The Stability

This paper develops some criteria for a kind of hybrid stochastic systems with time-delay, which improve existing results on hybrid systems without considering noises. The improved results show that the presence of noise is quite involved in the stability analysis of hybrid systems. New results can be used to analyze the stability of a kind of stochastic hybrid impulsive and switching neural networks (SHISNN). Therefore, stability analysis of SHISNN can be turned into solving a linear matrix inequality (LMI).

scholarly journals LMI-Based Approach for Exponential Robust Stability of High-Order Hopfield Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Yangfan Wang ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Robust Stability ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Global Exponential Robust Stability

This paper studies the problems of global exponential robust stability of high-order hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential robust stability for the high-order neural networks are established, which are easily verifiable and have a wider adaptive.

scholarly journals Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Wen-Jer Chang ◽  
Bo-Jyun Huang ◽  
Po-Hsun Chen
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Ship Steering

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

scholarly journals Low Conservative Criteria for Robust Consensus of Multiagent Systems with Delays, Disturbances, and Topologies Uncertainties

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Qingjie Zhang ◽  
Zhongqing Jin ◽  
Qiang Li ◽  
Jianwu Tao ◽  
Qiongjian Fan ◽  
...  
Keyword(s):  
Multiagent Systems ◽  
Robust Stability ◽  
Linear Matrix ◽  
Multiple Time ◽  
Matrix Inequality ◽  
Space Transformation ◽  
Strongly Connected ◽  
Nonlinear Matrix Inequality ◽  
The Stability ◽  
Robust Consensus

Considering the limited communications conditions such as delays, disturbances, and topologies uncertainties, the stability criteria for robust consensus of multiagent systems are proposed in this paper. Firstly, by using the idea of state decomposition and space transformation, the condition for guaranteeing consensus is converted into verifying the robust stability of the disagreement system. In order to deal with multiple time-varying delays and switching topologies, jointly quadratic common Lyapunov-Krasovskii (JQCLK) functional is built to analyze the robust stability. Then, the numerical criterion can be obtained through solving the corresponding feasible nonlinear matrix inequality (NLMI); at last, nonlinear minimization is used like solving cone complementarity problem. Therefore, the linear matrix inequality (LMI) criterion is obtained, which can be solved by mathematical toolbox conveniently. In order to relax the conservativeness, free-weighting matrices (FWM) method is employed. Further, the conclusion is extended to the case of strongly connected topologies. Numerical examples and simulation results are given to demonstrate the effectiveness and the benefit on reducing conservativeness of the proposed criteria.

Design of Control Laws Based on Inverted Decoupling and Linear Matrix Inequality for a Turboprop Engine

2020 ◽  
Vol 142 (2) ◽  
Author(s):  
Huairong Chen ◽  
Xi Wang ◽  
Meiyin Zhu ◽  
Nannan Gu ◽  
Shubo Yang
Keyword(s):  
Linear Matrix Inequality ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Shaft Speed ◽  
Blade Angle ◽  
Gas Generator ◽  
Control Laws ◽  
Control Loops ◽  
Turboprop Engine ◽  
Power Turbine

Abstract This paper proposes a systematic approach to design control laws for a turboprop engine. The proposed approach includes interactions decoupling and control laws design based on linear matrix inequality (LMI). First, since the main objective of the turboprop engine control system is to ensure propeller-absorbed power at a constant propeller speed, the linear model of a turboprop engine can be linearized into a two-input two-output (TITO) plants, and there exist the interactions between two control loops. Because inverted decoupling can well retain the dynamic characteristics of the original system, it is used to decouple the interactions so that the TITO plant can be divided into two single-input single-output plants, that is, gas-generator shaft speed is controlled by fuel flowrate and power turbine shaft speed is controlled by blade angle. Then, the control laws are designed separately for each control loop by solving the LMI group derived from static output feedback (SOF) and regional pole placement. Finally, the proposed approach is implemented on a two-spool turboprop engine (TSTPE) integrated model. The simulation results show that there exist strong interactions between two control loops of TSTPE, applying inverted decoupling to decouple these interactions is effective, and the gas-generator shaft speed and the power turbine speed can track their commands with appropriate performance by controlling the fuel flowrate and blade angle under the action of the designed control laws and inverted decoupling.

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