State feedback gain scheduling for linear systems with time-varying parameters

2004 ◽  
Author(s):  
V.F. Montagner ◽  
P.L.D. Peres
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Gain Scheduling ◽  
Feedback Gain ◽  
Time Varying ◽  
Varying Parameters ◽  
Time Varying Parameters

State Feedback Gain Scheduling for Linear Systems With Time-Varying Parameters

2005 ◽  
Vol 128 (2) ◽  
pp. 365-370 ◽  
Author(s):  
Vinícius F. Montagner ◽  
Pedro L. D. Peres
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Gain Scheduling ◽  
State Feedback Control ◽  
Feedback Gain ◽  
Structural Constraints ◽  
Time Varying ◽  
Varying Parameters ◽  
Time Varying Parameters ◽  
Parameter Dependent

This paper addresses the problem of parameter dependent state feedback control (i.e. gain scheduling) for linear systems with parameters that are assumed to be available (measured or estimated) in real time and are allowed to vary in a compact polytopic set with bounded variation rates. A new sufficient condition given in terms of linear matrix inequalities permits to determine the controller gain as an analytical function of the time-varying parameters and of a set of constant matrices. The closed-loop stability is assured by means of a parameter dependent Lyapunov function. The condition proposed encompasses the well-known quadratic stabilizability condition and allows to impose structural constraints such as decentralization to the feedback gains. Numerical examples illustrate the efficiency of the technique.

Pole Placement for Single-Input Linear System by Proportional-Derivative State Feedback

2014 ◽  
Vol 137 (4) ◽  
Author(s):  
Taha H. S. Abdelaziz
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Degrees Of Freedom ◽  
State Feedback ◽  
Pole Placement ◽  
Feedback Gain ◽  
Time Varying ◽  
Placement Problem ◽  
Single Input ◽  
Time Invariant

This paper deals with the direct solution of the pole placement problem for single-input linear systems using proportional-derivative (PD) state feedback. This problem is always solvable for any controllable system. The explicit parametric expressions for the feedback gain controllers are derived which describe the available degrees of freedom offered by PD state feedback. These freedoms are utilized to obtain closed-loop systems with small gains. Its derivation is based on the transformation of linear system into control canonical form by a special coordinate transformation. The solving procedure results into a formula similar to Ackermann’s one. In the present work, both time-invariant and time-varying linear systems are treated. The effectiveness of the proposed method is demonstrated by the simulation examples of both time-invariant and time-varying systems.

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