Beyond Interval Systems: What Is Feasible and What Is Algorithmically Solvable?

Some new criteria of delay-dependent stability for the switched time-delay uncertain system are deduced by employing time-switched method and the comparison theorem in this paper. The total activation time ratio of the switching law can be determined to guarantee the switched time-delay uncertain system is exponentially stable with stability margin . Finally, this method can be extended to switched interval systems with time-delay. Some examples are exploited to illustrate the proposed schemes..

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Controller design via model order reduction for interval systems using Kharitonov theorem and Nevalinna-pick theory: a case study

International Journal of System Control and Information Processing ◽

10.1504/ijscip.2021.10041143 ◽

2021 ◽

Vol 3 (3) ◽

pp. 193

Author(s):

V.P. Singh ◽

Dharma Pal Singh Chauhan

Keyword(s):

Model Order Reduction ◽

Controller Design ◽

Order Reduction ◽

Model Order ◽

Kharitonov Theorem ◽

Interval Systems

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On the Solutions of Interval Systems for Under-Constrained and Redundant Parallel Manipulators

Journal of Mechanisms and Robotics ◽

10.1115/1.4037803 ◽

2017 ◽

Vol 9 (6) ◽

Author(s):

Leila Notash

Keyword(s):

Least Squares ◽

Jacobian Matrix ◽

Parallel Manipulators ◽

Constrained Systems ◽

Solution Set ◽

Least Squares Solution ◽

Interval Linear ◽

Interval Linear Systems ◽

Parameter Dependency ◽

Interval Systems

For under-constrained and redundant parallel manipulators, the actuator inputs are studied with bounded variations in parameters and data. Problem is formulated within the context of force analysis. Discrete and analytical methods for interval linear systems are presented, categorized, and implemented to identify the solution set, as well as the minimum 2-norm least-squares solution set. The notions of parameter dependency and solution subsets are considered. The hyperplanes that bound the solution in each orthant characterize the solution set of manipulators. While the parameterized form of the interval entries of the Jacobian matrix and wrench produce the minimum 2-norm least-squares solution for the under-constrained and over-constrained systems of real matrices and vectors within the interval Jacobian matrix and wrench vector, respectively. Example manipulators are used to present the application of methods for identifying the solution and minimum norm solution sets for actuator forces/torques.

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