Above are papers related to the following paper: [Paper_ID] Paper #179702. 	[Title] FURTHER FACTS ABOUT INPUT TO STATE STABILIZATION "Further facts about input to state stabilization", IEEE [Abstract] Report SYCON-88-15 ABSTRACT Previous results about input to state stabilizability are shown to hold even for systems which are not linear in controls, provided that a more general type of feedback be allowed. Applications to certain stabilization problems and coprime factorizations, as well as comparisons to other results on input to state stability, are also briefly discussed. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1121569. 	[Title] A Characterization of Integral Input to State Stability [Abstract] Just as input to state stability (iss) generalizes the idea of finite gains with respect to supremum norms, the new notion of integral input to state stability (iiss) generalizes the concept of finite gain when using an integral norm on inputs. In this paper, we obtain a necessary and sufficient characterization of the iiss property, expressed in terms of dissipation inequalities. 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.

Above are papers related to the following paper: [Paper_ID] Paper #48555. 	[Title] FEEDBACK STABILIZATION USING TWO-HIDDEN-LAYER NETS [Abstract] This paper compares the representational capabilities of one hidden layer and two hidden layer nets consisting of feedforward interconnections of linear threshold units. It is remarked that for certain problems two hidden layers are required, contrary to what might be in principle expected from the known approximation theorems. The differences are not based on numerical accuracy or number of units needed, nor on capabilities for feature extraction, but rather on a much more basic classification into "direct" and "inverse" problems. The former correspond to the approximation of continuous functions, while the latter are concerned with approximating one-sided inverses of continuous functions |and are often encountered in the context of inverse kinematics determination or in control questions. A general result is given showing that nonlinear control systems can be stabilized using two hidden layers, but not in general using just one. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #7532. 	[Title] On Finite Gain Stabilizability of Linear Systems Subject to Input Saturation [Abstract] This paper deals with (global) finite-gain input/output stabilization of linear systems with saturated controls. For neutrally stable systems, it is shown that the linear feedback law suggested by the passivity approach indeed provides stability, with respect to every L p -norm. Explicit bounds on closed-loop gains are obtained, and they are related to the norms for the respective systems without saturation. These results do not extend to the class of systems for which the state matrix has eigenvalues on the imaginary axis with nonsimple (size &gt; 1) Jordan blocks, contradicting what may be expected from the fact that such systems are globally asymptotically stabilizable in the state-space sense; this is shown in particular for the double integrator. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #7537. 	[Title] Global Stabilization of Linear Discrete-Time Systems with Bounded Feedback [Abstract] This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time case by the authors, and shows that such stabilization is possible if and only if the system is stabilizable with arbitrary controls and the transition matrix has spectral radius less or equal to one. The proof provides in principle an algorithm for the construction of such feedback laws, which can be implemented either as cascades or as parallel connections ("single hidden layer neural networks") of simple saturation functions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #141171. 	[Title] New Characterizations of Input to State Stability [Abstract] We present new characterizations of the Input to State Stability property. As a consequence of these results, we show the equivalence between the ISS property and several (apparent) variations proposed in the literature. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #75318. 	[Title] A Smooth Converse Lyapunov Theorem for Robust Stability [Abstract] This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical theorems. In a unified and natural manner, it (1) allows arbitrary bounded time-varying parameters in the system description, (2) deals with global asymptotic stability, (3) results in smooth (infinitely differentiable) Lyapunov functions, and (4) applies to stability with respect to not necessarily compact invariant sets. 1. Introduction. This work is motivated by problems of robust nonlinear stabilization. One of our main Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #179706. 	[Title] Changing Supply Functions in Input/State Stable Systems [Abstract] We consider the problem of characterizing possible supply functions for a given dissipative nonlinear system, and provide a result that allows some freedom in the modification of such functions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152859. 	[Title] Reprint of: Sontag, E.D., "Remarks on stabilization and input-to-state stability," [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #424540. 	[Title] FEEDBACK STABILIZATION OF NONLINEAR SYSTEMS [Abstract] This paper surveys some well-known facts as well as some recent developments on the topic of stabilization of nonlinear systems. Please summarise all the given information.

Paper #179702 has the title `FURTHER FACTS ABOUT INPUT TO STATE STABILIZATION "Further facts about input to state stabilization", IEEE
` and the abstract `Report SYCON-88-15 ABSTRACT Previous results about input to state stabilizability are shown to hold even for systems which are not linear in controls, provided that a more general type of feedback be allowed. Applications to certain stabilization problems and coprime factorizations, as well as comparisons to other results on input to state stability, are also briefly discussed. 
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Question: Which category should Paper #179702 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #179702 has the title `FURTHER FACTS ABOUT INPUT TO STATE STABILIZATION "Further facts about input to state stabilization", IEEE
` and the abstract `Report SYCON-88-15 ABSTRACT Previous results about input to state stabilizability are shown to hold even for systems which are not linear in controls, provided that a more general type of feedback be allowed. Applications to certain stabilization problems and coprime factorizations, as well as comparisons to other results on input to state stability, are also briefly discussed. 
`.
Question: Which category should Paper #179702 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