Stability robustness analysis of state-space models for uncertain Linear time-varying systems

1994 ◽  
Vol 25 (12) ◽  
pp. 2221-2233 ◽  
Author(s):  
HONGSHENG XI
Keyword(s):  
State Space ◽  
Linear Time ◽  
Robustness Analysis ◽  
State Space Models ◽  
Time Varying ◽  
Stability Robustness ◽  
Time Varying Systems

$H^\infty $ Control of Linear Time-Varying Systems: A State-Space Approach

1991 ◽  
Vol 29 (6) ◽  
pp. 1394-1413 ◽  
Author(s):  
R. Ravi ◽  
K. M. Nagpal ◽  
P. P. Khargonekar
Keyword(s):  
State Space ◽  
Linear Time ◽  
Time Varying ◽  
State Space Approach ◽  
Time Varying Systems ◽  
Space Approach

Robust Adaptive Controllers for Interconnected Mechanical Systems: Influence of Types of Interconnections on Time-Invariant and Time-Varying Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 456-473 ◽  
Author(s):  
Sunil K. Singh ◽  
Lin Shi
Keyword(s):  
State Space ◽  
High Speed ◽  
Linear Time ◽  
Direct Method ◽  
Time Varying ◽  
Adaptive Controllers ◽  
First Order ◽  
Time Varying Systems ◽  
Robust Adaptive ◽  
Time Invariant

We investigate robust adaptive controller designs for interconnected systems when no exact knowledge about the structure of the nonlinear interconnections between various subsystems is available. In this study, we concentrate on several different types of systems. We deal with both linear time-invariant (LTI) and linear time-varying (LTV) systems with nonlinear interconnections. For LTI systems, we examine the following types of interconnections: • interconnections that are bounded by first order polynomials in state space; • slowly time varying interconnections; • interconnections bounded by higher-order polynomials in state-space together with input channel interconnections. For LTV systems we deal with interconnections bounded by first-order polynomials in state space. We show that the nature of the nonlinear interactions influences the adaptation laws. We use the direct method of Lyapunov for the design of adaptive controllers for tracking in such systems. We investigate issues such as stability, transient performance and steady-state errors, and derive quantitative estimates and analytical bounds for various different adaptive controllers. For time-varying systems, we analyze the effect of the time variations of parameters and interactions and propose a modified adaptive control scheme with better performance. Simulation results are presented to validate our conclusions. We also investigate these results experimentally on a two-link robot manipulator. Experimental results validate theoretical conclusions and demonstrate the usefulness of such robust adaptive controllers for high-speed motions in uncertain systems.

scholarly journals JOINT ESTIMATION OF STATES AND PARAMETERS OF LINEAR SYSTEMS WITH PARAMETER FAULTS UNDER NON-GAUSSIAN NOISES

2020 ◽  
Vol 18 (2) ◽  
pp. 113
Author(s):  
Vladimir Stojanović ◽  
Dragan Pršić ◽  
Ljubiša Dubonjić
Keyword(s):  
State Space ◽  
Stochastic Systems ◽  
Fault Tolerant ◽  
Linear Time ◽  
Practical Importance ◽  
Joint Estimation ◽  
State Space Models ◽  
Time Varying ◽  
Linear State ◽  
Non Gaussian

Joint estimation of states and time-varying parameters of linear state space models is of practical importance for the fault diagnosis and fault tolerant control. Previous works on this topic consider the joint estimation in the Gaussian noise environment, but not in the presence of outliers. The known fact is that the measurements have inconsistent observations with the largest part of the observation population (outliers). They can significantly make worse the properties of linearly recursive algorithms which are designed to work in the presence of Gaussian noises. This paper proposes the strategy of the joint parameter-state robust estimation of linear state space models in the presence of non-Gaussian noises. The case of parameter-dependent matrices is considered. Because of its good features in robust filtering, the extended Masreliez-Martin filter represents a cornerstone for realization of the robust algorithms for joint state-parameter estimation of linear time-varying stochastic systems in the presence of non-Gaussian noises. The good features of the proposed robust algorithm for joint estimation of linear time-varying stochastic systems are illustrated by intensive simulations.

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