Triangular orthogonal functions for the analysis of continuous time systems / Anish Deb, Gautam Sarkar, Anindita Sengupta.

Title from publisher's bibliographic system (viewed on 02 Oct 2015).

Ch. 1 Walsh, Block Pulse, and Related Orthogonal Functions in Systems and Control -- 1.1. Orthogonal Functions and their Properties -- 1.2. Different Types of Nonsinusoidal Orthogonal Functions -- 1.3. Walsh Functions in Systems and Control -- 1.4. Block Pulse Functions in Systems and Control -- 1.5. Conclusion -- References -- ch. 2 A Newly Proposed Triangular Function Set and Its Properties -- 2.1. Walsh Functions and Related Operational Matrix for Integration -- 2.2. BPFs and Related Operational Matrices -- 2.3. Sample-and-Hold Functions [9] -- 2.4. From BPF to a Newly Defined Complementary Set of Triangular Functions -- 2.5. Piecewise Linear Approximation of a Square Integrable Function f(t) -- 2.6. Orthogonality of Triangular Basis Functions -- 2.7. A Few Properties of Orthogonal TF -- 2.8. Function Approximation via Optimal Triangular Function Coefficients -- 2.9. Conclusion -- References -- ch. 3 Function Approximation via Triangular Function Sets and Operational Matrices in Triangular Function Domain -- 3.1. Approximation of a Square Integrable Time Function f(t) by BPF and TF -- 3.2. Operational Matrices for Integration in Triangular Function Domain -- 3.3. Error Analysis -- 3.4. Comparison of Error for Optimal and Nonoptimal Representation via Block Pulse as well as Triangular Functions -- 3.5. Conclusion -- References -- ch. 4 Analysis of Dynamic Systems via State Space Approach -- 4.1. Analysis of Dynamic Systems via Triangular Functions -- 4.2. Numerical Experiment [2] -- 4.3. Conclusion -- References -- ch. 5 Convolution Process in Triangular Function Domain and Its Use in SISO Control System Analysis -- 5.1. Convolution Integral -- 5.2. Convolution in Triangular Function Domain [3] -- 5.3. Convolution of Two Time Functions in TF Domain -- 5.4. Numerical Experiment -- 5.5. Integral Squared Error (ISE) in TF Domain and Its Comparison with BPF Domain Solution -- 5.6. Conclusion -- References -- ch. 6 Identification of SISO Control Systems via State Space Approach -- 6.1. System Identification via State Space Approach -- 6.2. Numerical Example [6] -- 6.3. Conclusion -- References -- ch. 7 Solution of Integral Equations via Triangular Functions -- 7.1. Solution of Integral Equations via Triangular Functions -- 7.2. Conclusion -- References -- ch. 8 Microprocessor Based Simulation of Control Systems Using Orthogonal Functions -- 8.1. Review of Delta Function and Sample-and-Hold Function Operational Technique -- 8.2. Microprocessor Based Simulation of Linear Single-Input Single-Output (SISO) Sampled-Data Systems [7] -- 8.3. Conclusion -- References.

This book deals with a new set of triangular orthogonal functions, which evolved from the set of well known block pulse functions (BPF), a major member of the piecewise constant orthogonal function (PCOF) family.