Robust Control of Switched Linear Systems via Min of Quadratics

2013 ◽  
Author(s):  
Chengzhi Yuan ◽  
Fen Wu
Keyword(s):  
Lyapunov Function ◽  
Linear Systems ◽  
Output Feedback Control ◽  
Control Design ◽  
Quadratic Functions ◽  
Linear Matrix ◽  
Switched Linear Systems ◽  
Synthesis Conditions ◽  
Arbitrary Switching ◽  
Special Cases

In this paper, we will investigate the robust switching control problem for switched linear systems by using a class of composite quadratic functions, the min (of quadratics) function, to improve performance and enhance control design flexibility. The robustness is reflected in two prospectives including the ℋ ∞ performance and arbitrary switching of subsystems. A hysteresis min-switching strategy is employed to orchestrate the switching among a collection of controllers. The synthesis conditions for both state feedback and output feedback control problems are derived in terms of a set of linear matrix inequalities (LMIs) with linear search over scalar variables. The proposed min function based approach unifies the existing single Lyapunov function based method and multiple Lyapunov function based method in a general framework, and the derived LMI conditions cover the existing LMI conditions as special cases. Numerical studies are included to demonstrate the advantages of the proposed control design approach.

H ∞ Control for Continuous-Time Switched Linear Systems

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Grace S. Deaecto ◽  
José C. Geromel
Keyword(s):  
Feedback Control ◽  
Linear Systems ◽  
Output Feedback ◽  
Continuous Time ◽  
Design Problem ◽  
State Feedback ◽  
Output Feedback Control ◽  
Control Design ◽  
Linear Matrix ◽  
Switched Linear Systems

This paper deals with the output feedback H∞ control design problem for continuous-time switched linear systems. More specifically, the main goal is to design a switching rule together with a dynamic full order linear controller to satisfy a prespecified H∞ level defined by the L2 gain from the input to the output signal. Initially, the state feedback version of this problem is solved in order to put in evidence the main difficulties we have to face toward the solution of the output feedback control design problem. The results reported in this paper are based on the so called Lyapunov–Metzler inequalities, which express a sufficient condition for switched linear systems global stability. The solution of the previously mentioned output feedback control design problem through a linear matrix inequality based method is the main contribution of the present paper. An academic example borrowed from literature is used for illustration.

New Results on Continuous-Time Switched Linear Systems With Actuator Saturation

2013 ◽  
Author(s):  
Chang Duan ◽  
Fen Wu
Keyword(s):  
Linear Systems ◽  
Differential Inclusion ◽  
Continuous Time ◽  
Actuator Saturation ◽  
Previous Method ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Switched Linear Systems ◽  
Synthesis Conditions ◽  
Lmi Optimization

This paper further studies the analysis and control problems of continuous-time switched linear systems subject to actuator saturation. Using the norm-bounded differential inclusion (NDI) description of the saturated systems and the minimal switching rule, a set of switched output feedback controllers is designed to minimize the disturbance attenuation level defined by the regional ℒ2 gain over a class of energy-bounded disturbances. The synthesis conditions are expressed as bilinear matrix inequalities (BMIs) and can be solved by numerical search coupled with linear matrix inequality (LMI) optimization. Compared to the previous method based on polytopic differential inclusion (PDI), the proposed approach has good scalability and potentially renders better performance. Numerical examples are provided to verify effectiveness of the proposed approach.

scholarly journals Fault Tolerant Control Design For Polytopic LPV Systems

2007 ◽  
Vol 17 (1) ◽  
pp. 27-37 ◽  
Author(s):  
Mickael Rodrigues ◽  
Didier Theilliol ◽  
Samir Aberkane ◽  
Dominique Sauter
Keyword(s):  
Output Feedback ◽  
Fault Tolerant ◽  
Output Feedback Control ◽  
Control Design ◽  
Fault Tolerant Control ◽  
Necessary Condition ◽  
Linear Matrix ◽  
Linear Parameter Varying ◽  
Lpv Systems ◽  
Static Output

Fault Tolerant Control Design For Polytopic LPV SystemsThis paper deals with a Fault Tolerant Control (FTC) strategy for polytopic Linear Parameter Varying (LPV) systems. The main contribution consists in the design of a Static Output Feedback (SOF) dedicated to such systems in the presence of multiple actuator faults/failures. The controllers are synthesized through Linear Matrix Inequalities (LMIs) in both fault-free and faulty cases in order to preserve the system closed-loop stability. Hence, this paper provides a new sufficient (but not necessary) condition for the solvability of the stabilizing output feedback control problem. An example illustrates the effectiveness and performances of the proposed FTC method.

Robust H∞ Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach

2005 ◽  
Vol 128 (3) ◽  
pp. 696-700 ◽  
Author(s):  
Zhijian Ji ◽  
Xiaoxia Guo ◽  
Long Wang ◽  
Guangming Xie
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Robust Stabilization ◽  
Disturbance Attenuation ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Multiple Lyapunov Functions ◽  
Switched Linear Systems ◽  
Switched State Feedback

This paper addresses robust H∞ control and stabilization of switched linear systems with norm-bounded time-varying uncertainties. First, based on multiple Lyapunov functions methodology, a sufficient condition is derived for robust stabilization with a prescribed disturbance attenuation level γ only by employing state-dependent switching rules. Then the robust H∞ control synthesis via switched state feedback is studied. It is shown that a switched state-feedback controller can be designed to stabilize the switched systems with an H∞-norm bound if a matrix inequality based condition is feasible. This condition can be dealt with as linear matrix inequalities (LMIs) provided that the associated parameters are selected in advance. All the results presented can be regarded as an extension of some existing results for both switched and nonswitched systems.

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