On computing maximum allowable time delay of Lur’e systems with uncertain time-invariant delays

2014 ◽  
Vol 12 (3) ◽  
pp. 497-506 ◽  
Author(s):  
Thapana Nampradit ◽  
David Banjerdpongchai
Keyword(s):  
Time Delay ◽  
Lur’E Systems ◽  
Uncertain Time ◽  
Time Invariant ◽  
Maximum Allowable Time

Supervisory Control of Dynamical Systems With Uncertain Time Delays

2009 ◽  
Author(s):  
Bo Song ◽  
Jian-Qiao Sun
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Supervisory Control ◽  
Time Delays ◽  
Linear Time ◽  
Theoretical Work ◽  
Linear Time Invariant ◽  
Uncertain Time ◽  
Linear Time Invariant System ◽  
Time Invariant

This paper presents a study of controlling dynamical systems with uncertain and varying time delays. We apply the supervisory control algorithm to handle uncertainties in time delay. The hysteretic switching rule selects control gains out of the set of pre-determined optimal feedback gains for certain time delays in a range with known lower and upper bounds. The criterion is to judge when the system stays stable for any gains being selected and has a smaller switching index when the uncertain time delay varies in a known interval. A linear time-invariant system is used as an example to demonstrate the theoretical work.

scholarly journals Robust Stabilization of Interval Plants with Uncertain Time-Delay Using the Value Set Concept

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 429
Author(s):  
Pedro Zamora ◽  
Alejandro Arceo ◽  
Noé Martínez ◽  
Gerardo Romero ◽  
Luis E. Garza
Keyword(s):  
Time Delay ◽  
Robust Stabilization ◽  
Parametric Uncertainty ◽  
Exclusion Principle ◽  
Control Synthesis ◽  
Classical Orthogonal Polynomials ◽  
Loop Control ◽  
Value Set ◽  
Interval Plants ◽  
Uncertain Time

This paper considers the robust stabilization problem for interval plants with parametric uncertainty and uncertain time-delay based on the value set characterization of closed-loop control systems and the zero exclusion principle. Using Kharitonov’s polynomials, it is possible to establish a sufficient condition to guarantee the robust stability property. This condition allows us to solve the control synthesis problem using conditions similar to those established in the loopshaping technique and to parameterize the controllers using stable polynomials constructed from classical orthogonal polynomials.

Complementary Sensitivity Design of PID Controllers for Arbitrary-Order Transfer Functions With Time Delay

2008 ◽  
Author(s):  
Tooran Emami ◽  
John M. Watkins
Keyword(s):  
Time Delay ◽  
Transfer Functions ◽  
Linear Time ◽  
Order System ◽  
Pid Controllers ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Plant Transfer ◽  
Time Invariant

A graphical technique for finding all proportional integral derivative (PID) controllers that stabilize a given single-input-single-output (SISO) linear time-invariant (LTI) system of any order system with time delay has been solved. In this paper a method is introduced that finds all PID controllers that also satisfy an H∞ complementary sensitivity constraint. This problem can be solved by finding all PID controllers that simultaneously stabilize the closed-loop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. A key advantage of this procedure is the fact that it does not require the plant transfer function, only its frequency response.

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