Above are papers related to the following paper: [Paper_ID] Paper #1114184. 	[Title] CONTROL-LYAPUNOV FUNCTIONS FOR TIME-VARYING SET STABILIZATION [Abstract] This paper shows that, for time varying systems, global asymptotic controllability to a given closed subset of the state space is equivalent to the existence of a continuous control-Lyapunov function with respect to the set. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #86923. 	[Title] Asymptotic Controllability Implies Feedback Stabilization [Abstract] | Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #18532. 	[Title] A REMARK ON ROBUST STABILIZATION OF GENERAL ASYMPTOTICALLY CONTROLLABLE SYSTEMS [Abstract] It was shown recently by Clarke, Ledyaev, Sontag and Subbotin that any asymptotically controllable system can be stabilized by means of a certain type of discontinuous feedback. The feedback laws constructed in that work are robust with respect to actuator errors as well as to perturbations of the system dynamics. A drawback, however, is that they may be highly sensitive to errors in the measurement of the state vector. This paper addresses this shortcoming, and shows how to design a dynamic hybrid stabilizing controller which, while preserving robustness to external perturbations and actuator error, is also robust with respect to measurement error. This new design relies upon a controller which incorporates an internal model of the system driven by the previously constructed feedback. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #18536. 	[Title] "UNIVERSAL" CONSTRUCTION OF ARTSTEIN'S THEOREM ON NONLINEAR STABILIZATION 1 [Abstract] Report SYCON-89-03 ABSTRACT This note presents an explicit proof of the theorem -due to Artstein- which states that the existence of a smooth control-Lyapunov function implies smooth stabilizability. More- over, the result is extended to the real-analytic and rational cases as well. The proof uses a "universal" formula given by an algebraic function of Lie derivatives; this formula originates in the solution of a simple Riccati equation. Please summarise all the given information.

Paper #1114184 has the title `CONTROL-LYAPUNOV FUNCTIONS FOR TIME-VARYING SET STABILIZATION  
` and the abstract `This paper shows that, for time varying systems, global asymptotic controllability to a given closed subset of the state space is equivalent to the existence of a continuous control-Lyapunov function with respect to the set. 
`.
Question: Which category should Paper #1114184 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1114184 has the title `CONTROL-LYAPUNOV FUNCTIONS FOR TIME-VARYING SET STABILIZATION  
` and the abstract `This paper shows that, for time varying systems, global asymptotic controllability to a given closed subset of the state space is equivalent to the existence of a continuous control-Lyapunov function with respect to the set. 
`.
Question: Which category should Paper #1114184 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks